fulvio gismondi

Ha pubblicato volumi e comunicazioni scientifiche che possono essere classificati principalmente   nell’ambito della Teoria del Rischio e dei Processi Stocastici, della Matematica Finanziaria e della Matematica Attuariale. L’attività di ricerca ha riguardato processi di valutazione, modelli e soluzioni operative

[65]“ Insurance contracts for hedging wind power uncertainty ”

Mathematics, 2020, 8. 1376; DOI: 10.3390/math8081376 (with G. D’Amico, F. Petroni)

Abstract. This paper presents an insurance contract that the supplier of wind power may subscribe to with an insurance company in order to immunize his/her revenue against the volatility of wind power and prices. Based on empirical evidence, we found that wind power and electricity prices are correlated. Then, we adopted a joint stochastic process to model both time series, which is based on indexed semi-Markov chains for the wind power generation process and on a general Markovian process for the electricity price process. Using a joint stochastic model allows the insurance company to compute the fair premium that the wind power producer has to pay in order to hedge the risk against inadequate revenues. Recursive type equations are obtained for the prospective mathematical reserves of the insurance contract. The model and the validity of the results are illustrated through a real data application.

[64]“ A new approach to the modeling of financial volumes ”

Stochastic Processes and Application, Springer, January 2019 (with G. D’Amico, F. Petroni)

Abstract. In this paper we study the high frequency dynamic of financial volumes of traded stocks by using a semi-Markov approach. More precisely we assume that the intraday logarithmic change of volume is described by a weighted-indexed semi-Markov chain model. Based on this assumptions we show that this model is able to reproduce several empirical facts about volume evolution like time series depen¬dence, intra-daily periodicity and volume asymmetry. Results have been obtained from a real data application to high frequency data from the Italian stock market from first of January 2007 until end of December 2010.

[63]“ Stock market daily volatility and information measures of predictability ”

Physica a: Statistical Mechanics and its Applications, DOI:10.1016/j.physa.2018.11.049, November 2018 (with G. D’Amico, F. Petroni, F. Prattico)

Abstract. The main purpose of this work is to investigate the relation between some measures in information theory and the accuracy of volatility forecasting using a model of asset returns. First we highlight the dependence between volatility forecasting and entropy and then we determine the relation between predictability and volatility. The study is conducted using a database of 65 stocks of the Dow Jones Composite Average from 1973 to 2014 and by computing the daily volatility of-the market index. To this end we use the standard GARCH approach to model and forecast the daily volatility. The main result of this paper is the establishment of a relationship between the accuracy of the volatility forerecast and the entropy of the time series of price returns. Since the entropy changes in time, before computing a forecast of the volatility it is recommended to compute the entropy of the time series that furnishes an important indicator on the limit of successive volatility forecast.

[62]“ The calculation of Pure Premium for Health Insurance by Non-Homogeneous Semi-Markov Reward Processes ”

42° Convegno Amases, Napoli, 13-15 September 2018 (with G. D’Amico J. Jansen, R. Manca, D. Silvestrov, E. Volpe di Prignano)

[61]“ Insurance contracts for Hedging wind power uncertainty ”

International Workshop on Applied Probability”, Budapest, 18-21 June 2018 (with G. D’Amico, F. Petroni)

Abstract. Wind energy is assuming even more importance in the production of electricity. The share of production due to wind is continuously increasing in time although there are still relevant problems that affect this industry. The most important limitation for a further development of the wind energy industry concerns the variability of the wind speed phenomenon. The problem of the wind speed volatility has been approached mainly by energy storage systems; that is, by storing a surplus of energy to be used for compensating an eventual future deficit of production. More recently an insurance contract between the wind energy producer and a dispatchable energy producer has been proposed as a mean to manage the uncertainty of the wind speed. In this paper we extend previous results involving the use of insurance contracts by considering the dependence existing between electricity prices and wind energy production. The dependence structure is modeled using an appropriate copula function and we show the the impact of this dependence on the fair premium that the wind power supplier has to pay in order to hedge the risk of inadequate output of electricity at any time. Recursive type equations are obtained for the prospective mathematical reserves of the insurance contract and for their higher order moments. The model and the validity of the results are illustrated through a numerical example.

[60]“ A Non-Homogeneous Semi-Markov Model for the Calculation of the claim reserving of a Health Fund ”

Stochastic Modeling Techniques & Data Analysis International Conference, Chania, Crete, 12-15 June 2018 (with G. D’Amico, M. Guillen, J. Jansen, R. Manca, E. Volpe di Prignano) ISBN:978-618-5180-27-0

Abstract. This paper will present a model that gives the possibility of the calculation of the expenses of a health insurance fund without considering the administrative costs. To get this result we subdivide the insured people in cohorts. We will follow, for each cohort, the evolution of the costs of claims of the fund.
We will work in Non-Homogenous Semi-Markov setting considering also the ReWard Process with Backward recurrent time (see Stenberg net al (2007) and (D’Amico et al. (2010)).
The time variable that we consider is the age. Indeed, it is easily understood that an illness has different evolutions depending on the age of the insured. It is natural supposing that the illness evolution is function of the different age and illness and it will not change too much in different calendar times at a given age.

[59]“ Optimal provision of a dispatchable energy source for wind energy management: dependence on the wind energy model ”

Stochastic Modeling Techniques & Data Analysis International Conference, Chania, Crete, 12-15 June 2018 (with G. D’Amico, F.Petroni) ISBN:978-618-5180-27-0

Abstract. Wind energy is assuming even more importance in the production of electricity. The share of production due to wind is continuously increasing in time although there are still relevant problems that affect this industry The most important limitation for a further development of the wind energy industry concerns the variability of the wind speed phenomenon.
The problem of the wind speed volatility has been approached mainly by energy storage systems; that is, by storing a surplus of energy to be used for compensating an eventual future deficit of production. More recently an insurance contract between the wind energy producer (WEP) and a dispatchable energy producer (DEP) has been proposed as a mean to manage the uncertainty of the wind speed.
in this paper we assume that the WEP is also able to produce energy by means of gas and that he has agreed to furnish a given quantity of energy K. An insufficient production of energy determines a cost to be suffered because penalties apply. However, an excess of production is lost Therefore, the energy producer should determine the optimal quantity of energy to be produced with gas that added to the uncertain wind energy production maximize his expected profit. The problem is solved under different hypothesis on the wind energy model. First, the wind energy production is modelled by a simple sequence of i.i.d. random variables, then a Markov chain model is used and finally semi-Markov based models of wind energy are applied. The results show the dependence of the optimal policy on the different models of wind energy and therefore highlight the importance of using an appropriate model of wind energy. The application is performed on real data of energy produced by a wind turbine E-48 ENERCON of rated power 800kW.

[58]“ Reducing wind power uncertainty using insurance contracts ”

Stochastic Modeling Techniques & Data Analysis International Conference, Chania, Crete, 12-15 June 2018 (with G. D’Amico, F. Petroni) ISBN:978-618-5180-27-0

Abstract. The share of electricity production due to wind is continuously increasing although relevant problems still affect this industry. The most important limitation for a further development of the wind energy industry concerns the variability of the wind speed phenomenon. The problem of the wind speed volatility has been approached mainly by energy storage systems, that is, by storing a surplus of energy to be used for compensating an eventual future deficit of production. More recently an insurance contract between the wind energy producer and a dispatchable energy producer has been proposed as a mean to manage the uncertainty of the wind speed. In this paper we extend previous results involving the use of insurance contracts by considering the dependence existing between electricity prices and wind energy production. The dependence structure is modeled using an appropriate copula function and we show the impact of this dependence on the fair premium that the wind power supplier has to pay In order to hedge the risk of inadequate output of electricity at any time. Recursive type equations are obtained for the prospective mathematical reserves of the insurance contract and for their higher order moments The model and the validity of the results are illustrated through a numerical example.

[57]“ The Study of basic risk processes by discrete-time non-homogeneous Markov processes ”

Theory of Probability and Mathematical Statistics, Volume 96, 2017 (with G. D’Amico, J. Janssen, R. Manca, F. Petroni, E. Volpe di Prignano)

Abstract. This paper elaborates how it is possible to calculate precisely the aggregate claim amount and the claim number by means of Markov reward models in a non-homogeneous time setting. More precisely, evolution equations of the non-homogeneous Markov reward processes are presented in a discounted environment for the calculation of the aggregate claim amount and in a non-discounted case for the calculation of the claim number. The underlying Markov process has a denumerable number of states. In the last section, an application of the proposed models is presented using real data obtained by merging databases of two small insurance companies. The results highlight the importance of the insured’s age in the calculation of the actuarial quantities.

[56]“ A non-homogeneous semi-Markov approach for the calculation of the balance sheet of a health fund ”

International Actuarial Association Conference – Life Section, Barcelona, 23-24 October 2017 (with G. D’Amico, M. Guillen, J. Janssen, R. Manca, E. Volpe di Prignano)

Abstract. This paper presents a model that permits the calculation of the balance sheet of a health fund without taking into account the administrative costs.
Having to follow the evolution of the entrance and the expenses of the fund we present a two non-Homogenous Semi-Markov ReWard Process (NHSMRWP) (see Janssen & Manca 2006, 2007) in which the first (NHSMRWP) will follow the entrances and the second will consider the expenses of the fund. For each insured of a given age and sex will be obtained the pure premium.
The non-homogenous time variable that will be considered is the age. Indeed, it is easy to understand that the impact of an illness will have different reactions depending on the age of the sick person. For two insureds having the same age at different times it is possible to suppose that the behaviour of the illness evolution will not change too much.
The pure premium will take into account also the different costs that the insurance company will pay depending on the different age and illness.

[55]“ Long Term saving in an ageing world ”

International Actuarial Association Conference – Life Section, Barcelona, 23-24 October 2017 (with G. D’Amico, M. Guillen, J. Janssen, R. Manca, E. Volpe di Prignano)

[54]“ The calculation of pure premium for non-life insurance by generalized non-homogeneous Markov reward processes ”

International conference on Stochastic Processes and Algebraic Structures, Stockholm, 4-6 October 2017 (with G. D’Amico, M. Guillen, J. Janssen, R. Manca, E. Volpe di Prignano)

Abstract. Starting from the seminal paper Lundberg (1903) many papers tried to obtain reliable models for the calculation of the aggregate claim amount and the claim number for insurance contract. On this topic we recall also the papers by Cramer (1930,1955), De Finetti (1940).
This paper will explain how it is possible in a simple and reliable way to obtain, once that the aggregate claim amount is calculated, the pure premium for health insurance by means of a non-homogeneous Semi-Markov reward process.
In the paper the age is considered as the non-homogeneous time variable.

• Stochastic processes
• Health insurance

and their applications in

• Pure premium
• Insurance

[53]“ Hitting times for claim number in car insurance setting ”

Applied Stochastic Models and Data Analysis International Conference, London, 6-9 June 2017 (with G. D’Amico, J. Janssen, R. Manca, F. Petroni, D. Silvestrov)

Abstract. In this paper, the phase space of non-homogeneous semi-Markov processes is constructed taking into account the number of claims that an insured will have during her/his driving life. The aim is the calculation, for a driver, of the mean time to report a given number of claims. This problem can be solved constructing the probability distribution function of the first entry time for each state (number of claims) of the model. The age is considered as the non-homogeneous time variable.
As well known, the age in car insurance contracts plays a fundamental relevance in the calculation of behaviour of insured people. In this study, non-homogeneous semi-Markov models will be used for following the time evolution of the claim number.

[52]“Discrete time non-homogeneous compound renewal processes: a motor car insurance application”

European Actuarial Journal Conference, Lyon 5-8 settembre 2016 (with G. D’Amico, J. Janssen, and R. Manca)

Abstract. The age of insured people has great relevance in actuarial problems. The consideration of the age in insurance application implies the construction of non-homogeneous models. Renewal theory has many applications in actuarial science. Furthermore, in actuarial problems the financial aspects assumes a fundamental role in the construction of insurance models. All these considerations bring to the necessity of the systematisation of non-homogeneous compound renewal process and this is the aim of this paper.

After the definition of non-homogeneous compound process, the paper shows all the strictly interactions between these process and the non-homogeneous convolutions. As in Markov and semi-Markov reward processes, the compound renewal process are a family of stochastic processes which evolution equations depend on the hypotheses of the model that should be constructed. In the paper some of these evolution equations will be presented, it will be also explained how to get some other evolution equation. In the last part of the paper an application of models will be presented. Indeed, non-homogeneous compound renewal processes are not yet well established introduction of non-homogeneity in the renewal processes brings actuarial applications closer to the real world. This paper will follow the definition of time non-homogeneous convolutions given by the authors in another paper and try to systematize the non-homogeneous compound renewal processes. The numerical aspects of these process are dealt with and, finally, a real data application to an aspect of motorcar insurance is proposed.

[51] “Non-homogeneous discrete time alternating renewal processes for health insurance evolution and evaluation”

St. John’s Colloquium, International Pension and Employee Benefits Lawyers Association, St. John, 26-29 giugno 2016 (with G. D’Amico, J. Janssen, F. Petroni, R. Manca and E. Volpe di Prignano)

Abstract. Non homogeneous setting, with age as time variable and with sufficient data, it will be possible the construction of non-parametric models. The same holds with seniority as time variable.

Non-homogeneous environment with running time variable needs many data because of construction of the sequence of parameters. If there are few data it could be better using a homogeneous model.
Homogeneous environment for the construction of non-parametric model asks less data because it gives less results. If data are not enough also for a non parametric homogeneous model it could be construct a homogeneous parametric model.
The contracts for health and temporary disability insurance have two possible states health or ill (disable). When the insured is healthy then he will pay the premium to the insurance company. If he is ill then he will receive the claim, payments by the insurance company. The kind of the payment that he will receive will be function of contract. Certainly, he will receive the reimbursement of the expenses that he will pay because of the illness. Furthermore, he could receive for each day or week or month a sum of money.

[50] “Basic risk processes in a non-homogeneous markov chains setting”

International Workshop on Applied Probability”, Toronto 20-23 giugno 2016 (with G. D’Amico, J. Janssen, and R. Manca)

Abstract. As it is well known, the age in insurance contracts plays a fundamental relevance in the calculation of premiums. In this study, non-homogeneous Markov models useful for following the time evolution of the aggregate claim amount and the claim number in insurance setting are presented. More precisely the non-homogeneous Markov reward processes in both discounted and not discounted cases are applied to solve the aggregate claim amount and the claim number processes, respectively. Non-homogeneity gives the possibility of taking into account the age of the insured people.
In the last section the application of the proposed models is presented.

[49] “Study of human migration into EU area: a semi-markov approach”

Stochastic Modeling Techniques & Data Analysis International Conference”, Malta 1-4 giugno 2016 (with G. D’Amico, J. Janssen, R. Manca and D. Strangio)

Abstract. It is well known that the migration models could be well studied by means of a semi-Markov process because this tool permits to take into account of the flux but also of waiting time, in this case, inside a country.

In this period, given the serious political problems in African and Middle East countries, the migration into some countries of EU increased in a substantial way. In this study, we will classify the countries that are interested to this phenomenon in starting, transient and arriving countries. We will also take in great relevance the mean waiting times in each transient and arriving state. We will give also the probabilities of

migration among the interested countries and, furthermore, the calculation of the mean time that is necessary for the arrival into the final destination.

[48] “Homogeneous discrete time alternating compound renewal process: a disability insurance application”

in Mathematical Problems in Engineering, ISSN: 1024-123X, June 2015 (with G. D’Amico, J. Janssen and R. Manca)

Abstract. Discrete time alternating renewal process is a very simple tool that permits solving many real life problems. This paper, after the presentation of this tool, introduces the compound environment in the alternating process giving a systematization to this important tool. The claim costs for a temporary disability insurance contract are presented. The algorithm and an example of application are also provided.

[47] “Stochastic cash flows modeled by homogeneous and non-homogeneous discrete time backward semi-Markov reward processes”

in Statistic and Operations Research Transaction, p. 107-138, ISSN: 1696-2281, July-December 2014 (with J. Janssen, R. Manca and E. Volpe di Prignano)

Abstract. The main aim of this paper is to give a systematization on the stochastic cash flows evolution. The tools that are used for this purpose are discrete time semi-Markov reward processes. The paper is directed not only to semi-Markov researchers but also to a wider public, presenting a full treatment of these tools both in homogeneous and non-homogeneous environment. The main result given in the paper is the natural correspondence of the stochastic cash flows with the semi-Markov reward processes. Indeed, the semi-Markov environment gives the possibility to follow a multi-state random system in which the randomness is not only in the transition to the next state but also in the time of transition. Furthermore, rewards permit the introduction of a financial environment into the model. Considering all these properties, any stochastic cash flow can be naturally modelled by means of semi-Markov reward processes. The backward case offers the possibility of considering in a complete way the duration inside a state of the studied system and this fact can be very useful in the evaluation of insurance contracts.

[46] “Discrete time non-homogeneous compound renewal processes: a motor car insurance application”

Applied Stochastic Models and Data Analysis International Conference, Pireo, 30 giugno – 4 luglio 2015 (with G. D’Amico, J. Janssen and R. Manca)

Abstract. The age of insured people has great relevance in actuarial problems. The consideration of the age in insurance applications implies the construction of non-homogeneous models. Renewal theory has many applications in actuarial science. Furthermore, in actuarial problems the financial aspects assumes a fundamental role in the construction of insurance models. All these considerations bring to the necessity of the systematisation of non-homogeneous compound renewal process and this is the aim of this paper. After the definition of non-homogeneous compound process, the paper shows all the strictly interactions between these process and the non-homogeneous convolutions. As in Markov and semi-Markov reward processes, the compound renewal process are a family of stochastic processes which evolution equations depend on the hypotheses of the model that should be constructed. Some of these evolution equations will be presented, it will be also explained how to get some other evolution equation. An application of models will be presented. Indeed, non-homogeneous compound renewal processes are not yet well established introduction of non-homogeneity in the renewal processes brings actuarial applications closer to the real world. The numerical aspects of these process are dealt with and, finally, a real data application to an aspect of motorcar insurance is proposed

[45] “Discrete time alternating compound renewal process; a disability insurance application”

Mathematical and Statistical Methods for Actuarial Sciences and Finance, Salerno, 22-24 aprile 2014 (with G. D’Amico, J. Janssen and R. Manca)

Abstract. Discrete time alternating renewal process is a very simple tool that permits to solve many real life problems. This paper, after the presentation of this tool, introduces the compound environment in the alternating process. The calculation of the claim costs for a temporary disability insurance contract is presented. The algorithm and an example of application is also provided.

[44] “Non homogeneous time convolutions, renewal processes and age dependent mean number of motorcar accidents”

in Annals of Actuarial Science, ISSN: 1748-4995, doi: 10.1017/S1748499514000220, August 2014 (with J. Janssen and R. Manca)

Abstract. Non-homogeneous renewal processes are not yet well established. One of the tools necessary for studying these processes is the non-homogeneous time convolution. Renewal theory has great relevance in general in economics and in particular in actuarial science, however, most actuarial problems are connected with the age of the insured person. The introduction of non-homogeneity in the renewal processes brings actuarial applications closer to the real world. This paper will define the non-homogeneous time convolutions and try to give order to the non-homogeneous renewal processes. The numerical aspects of these processes are then dealt with and a real data application to an aspect of motorcar insurance is proposed.

[43] “Discrete time homogeneous Markov processes for the study of basic risk processes” in Methodology and Computing in Applied Probability”

ISSN: 1387-5841, doi: 10.1007/S11009-014-9416-5, July 2014 (with G. D’Amico, J. Janssen and R. Manca)

Abstract. In this paper Markov models useful for following the time evolution of the aggregate claim amount and the claim number in the homogeneous time environment are presented. More precisely the homogeneous Markov reward processes in both discounted and not discounted cases are applied to solve the aggregate claim amount and the claim number processes respectively. In the last section the application of the proposed models is presented. Two different real-world databases are mixed for the construction of input data.

[42] “Disability insurance claims study by a homogeneous discrete time alternating renewal processes”

in Modern Problem in Insurance Mathematics, Springer, ISBN: 978-3-319-06652-3, 2014 (with G. D’Amico, J. Janssen and R. Manca)

Abstract. The discrete time alternating renewal process is a very simple tool that enables the solution of many real life problems. After presenting this tool, we propose its application to compute the mean number of claims for a temporary disability insurance contract. The algorithm and an example of its application will also be provided.

[41] “The input evaluation of generalized Bernoulli processes for salary lines construction by means of continuous time generalized non-homogeneous semi-Markov processes”

Communications in Statistics Theory and Method, vol. 42, p. 2889-2901, ISSN: 0361-0926, 2013, doi:10.1080/03610926.2012.745558 (with G. D’Amico, G. Di Biase and R. Manca)

Abstract. Salary line forecasting assumes a relevant role in manpower and in pension funds Previously, the authors presented a generalized Bernoulli process, useful for forecasting the evolution of salary lines, taking into account the salary costs, the number of workers at each rank and the probability transitions between the ranks. The problem with applying this model is constructing the probability of transition between the grades. In this article, we will present a model that allows obtaining these probabilities by means of the solution of the evolution equation of a generalization of continuous time non-homogeneous semi-Markov processes.

[40] “Discrete time non-homogeneous compound renewal processes for G/G risk model solution”

International Cramer Symposium on Insurance Mathematics, International Cramer Symposium on Insurance Mathematics, Stockholm, 2013 (with J. Janssen e R. Manca)

Abstract. In this paper we define the discrete time non-homogeneous compound renewal process. This tool will be applied for the solution of the G/G risk model defined in Andersen (1967). The algorithm for solving this process will be also presented. In the last part of the paper the application of G/G model will be applied to a disability insurance problem.

[39] “IBNyR claims study by an alternating renewal process approach”

International Cramer Symposium on Insurance Mathematics, Stockholm, 2013 (with J. Janssen, F. Petroni and R. Manca)

Abstract. The problem of the evaluation of the IBNyR claims and of their properties is one of the most tortuous problem for the evaluation of claim reserving problems. In this paper we will evaluate all the probabilities properties of the IBNyR claim evolution by applying, for the first time in this topic, the alternating renewal process.

[38] “Discrete time homogeneous semi-Markov Monte Carlo reward risk process”

International Cramer Symposium on Insurance Mathematics, Stockholm, 2013 (with J. Janssen, R. Manca and D. Silvestrov)

Abstract. In this paper a semi-Markov process useful for following the time evolution of the aggregate claim amount in a homogeneous environment is defined. A mixture between the semi-Markov process and the Monte Carlo simulation model for the evaluation of the rewards paid by an insurance company for the claims permits the evaluation of the aggregate claim amount for each ensured of the company. Once the semi-Markov process is solved a Monte Carlo model is activated. By means of this simulation process the values of claim rewards will be calculated. The states of process will be given by classes of money amount. In the reconstruction of trajectories by the Monte Carlo method the semi-Markov and the simulation algorithm will interact influencing the trajectory reconstruction.

[37] “Homogeneous and non-homogeneous risk theory renewal models”

International Conference Probability Theory and its Applications, Moskow, 2012 (with G. D’Amico, J. Janssen and R. Manca)

Abstract. In Lundberg (1909) the foundation of the models for the study of risk theory and in the same time of renewal processes were done. The Poisson-Poisson model (P/P) was proposed. It names in this way because it is supposed that the mean number of claims and their cost follow a Poisson distribution. Cramer (1955) generalized the P/P model defining a P/G model where G stay for general type of distribution. At last Andersen (1967) defined the G/G model. The G/G model is closer to real life insurance problems, but it is really difficult to apply. All the three models are defined in a time homogeneous environment. In each insurance contract the age of insured assumes a great relevance, but in a homogeneous environment it is not possible to take into account this relevant aspect. In Janssen, Manca (2007) it is shown how to solve numerically a homogeneous renewal process and that the renewal process can be easily solved in a discrete time environment. In the first part of this paper will be presented how to solve the G/G model in discrete time setting. Furthermore, following the results obtained in Janssen et al (2011) it will be shown how to generalize in a discrete time non-homogeneous environment the G/G model. Given that the claim amount process is function of the economic scenario, the non-homogeneity is strictly related to the time of the evaluation.

[36] “Homogeneous and non-homogeneous G/G discrete time risk models: an algorithmic approach”

Applied Stochastic Models and Data Analysis (ASMDA 2011), Rome, 2011 (with J. Janssen, R. Manca, G. Ventura)

Abstract. In Lundberg (1909) the foundation of the models for the study of risk theory and in the same time of renewal processes were done. The Poisson-Poisson model (P/P) was proposed. It names in this way because it is supposed that the mean number of claims and their cost follow a Poisson distribution. Cramer (1955) generalized the P/P model defining a P/G model where G stay for general type of distribution. At last Andersen (1967) defined the G/G model.
The G/G model is closer to real life insurance problems, but it is really difficult to apply. All the three models are defined in a time homogeneous environment. In each insurance contract the age of insured assumes a great relevance, but in a homogeneous environment it is not possible to take into account this relevant aspect.
In Janssen, Manca (2007) it is shown how to solve numerically a homogeneous renewal process and that the renewal process can be easily solved in a discrete time environment.
In the first part of this paper will be presented how to solve the G/G model in discrete time setting. Furthermore, following the results obtained in Janssen et al (2011) it will be shown how to generalize in a discrete time non-homogeneous environment the G/G model. Given that the claim amount process is function of the economic scenario, the non-homogeneity is strictly related to the time of the evaluation.

[35] “The construction of claim reserve distribution by means of a Semi-Markov Backward Simulation Model”

Annals of Actuarial Science, vol. 6, p. 23-64, ISSN: 1748-4995, doi: .10.1017/S1748499511000315, 2011 (with J. Janssen and R. Manca)

Abstract. The claims reserving problem is currently one of the most debated in actuarial literature. The high level of interest in this topic is due to the fact that Solvency II rules will come into operation in 2014. Indeed, it is expected that quantile computations will be compulsory in the evaluation of company risk and for this reason we think that the construction of the claims reserve random variable distribution assumes a fundamental relevance. The aim of this paper is to present a method for constructing the claims reserve distribution which can take into account IBNyR (Issued But Not yet Reported) claims in a natural way. The construction of the distribution function for each time of the observed interval is done by means of a Monte Carlo simulation model applied on a backward time semi-Markov process. It should be pointed out that this is the first time that a simulation model based on semi-Markov with backward recurrence time has been presented. The method is totally different from the models given in the current literature.The most important features given in the paper are: 1) for the first time the Monte Carlo simulation method is applied to a backward semi-Markov environment; 2) the Monte Carlo simulation permits the construction of the random variable of the claims reserve for each year of the studied horizon in a natural way; 3) as already pointed out, the backward process attached to the semi-Markov process permits taking into account the evaluation of the IBNyR claims in a natural way. In the last part of the paper an applicative example constructed from tables that summarise 4 years of claims from an important Italian insurance company will be given.

[34] “Il sistema contributivo: questo sconosciuto”

in M. Marè (Curatore), “La previdenza complementare: quale futuro?”l Mulino, Bologna 2011 (in collaborazione con S. Gronchi)

Abstract. Il contributo al volume collettaneo esordisce con una disamina del contesto internazionale in cui, negli anni ’90, nasce, in Europa, l’idea ‘contributiva’ in risposta alle istanze di equità e sostenibilità dei sistemi pensionistici a ripartizione. Affronta quindi quattro questioni analiticamente circoscritte.

In primo luogo, sono esaminate le ragioni per cui i coefficienti di trasformazione di tipo ‘erga omnes’ (adottati in Italia) non consentono l’equità e sono proposti, in sostituzione, coefficienti diversificate per coorte dei quali sono spiegate le corrette modalità di aggiornamento.

In secondo luogo, sono discussi i fenomeni redistributivi che lo schema NDC produce in presenza di rendite reversibili e sono proposti correttivi per la loro eliminazione.

In terzo luogo, sono discusse le ragioni per cui l’indicizzazione delle rendite ‘non canonica’ (incoerente con i coefficienti di trasformazione) adottata dallo schema NDC italiano contraddice il principio di corrispettività ed è proposto un correttivo.

[33] “Salary lines forecasting by means of generalized binomial processes”

International Journal of Management Science and Engineering Management, vol. 5, p. 310-321, ISSN: 1750-9653, DOI: 10.1080/17509653.2010.10671122, 2010 (with R. Manca and A.V. Swishchuk)

Abstract. The evolution salary is function of the rules of career development. These rules usually change if the company being observed changes. With this fact in mind, this paper presents a class of useful models for forecasting the number of workers at each grade of a given firm. The paper generalizes the results obtained in some previous papers giving, for the first time, the possibility of forecasting not only the cost of the salary but also its subdivision into its constituents parts both for the total and the unitary wage cost. The model also permits the forecasting of the future career path of the workers in each grade and also the taking in account the future gender percentage within the different grades. Furthermore, the model presented offers the possibility of considering the changes in the job pyramidal structure considering also the change of the number of grades of the studied firm. A real data application is presented in which different hypotheses of the future evolution of the labour force are shown. The related algorithm is also presented.

[32] “A Monte Carlo semi-Markov backward model for a distributional claim reserve construction”

International Workshop on Applied Probability (IWAP 2010), Universidad Carlos III De Madrid, Madrid, 2010 (with J. Janssen and R. Manca)

Abstract. The claim reserving problem is currently one of the most debated in actuarial literature;

The high level of interest in this topic is due to the fact that Solvency II rules were approved in May 2009 and will come into operation in 2012. In that data the rule that establishes having the accumulated capital necessary to limit the risk failure fixed at 0.005 probability will be compulsory. For this reason the reconstruction of the claim reserve random variable distribution assumes a fundamental relevance.

The aim of this paper is to present a method that is able to reconstruct the claim reserve distribution and that can take into account, in a natural way, the IBNyR (Issued But Not yet Reported) claims. The proposed method is totally different from the models that are typically used in these problems given in the current literature.

[31] “The claim reserve as a company insurance reliability measure”

International Symposium on Stochastic Models in reliability Engineering, Life Sciences and Operations Management (SMRLO), Beer Sheva, Israel, 2010 (with J. Janssen and R. Manca)

Abstract. The claim reserve is one of the problems most debated in the actuarial literature (in the ASTIN last issue 4 papers were on this topic). The claim reserve should be considered a tool able to reduce the default risk of an insurance company that means its reliability.

For this reason we retain that the claim reserve should be function of the rating evaluation given to the insurance company.

This paper would face this kind of problem and report the first results on this new approach to the claim reserve problem.

[30] “Application of parallel grammatical evolution to the generation of automatic trading systems”

International Finance Symposium 2009, Istanbul, 2009 (with R. Gismondi, W. Janko e P. Kreuzinger)

Abstract. This paper investigates the applicability of automated trading systems for the DAX Future, which were generated using a parallelized form of grammatical evolution and historic market data. The included test results are based on a single-CPU algorithm and a parallelized version, which was run on a cluster of the Research Institute for Computational Methods of the Vienna University of Economics and Business. The single-CPU algorithm employs a genetic algorithm library called GALIb, written at the Massachusetts Institute of Tecnology (MIT) and extended by Matthew Wall, as search engine and a grammatical evolution library called libGE, written by Miguel Nicolau and Darwin Slattery, that maps genotype representations from GALIb onto trading rules and evaluates their fitness using three different evaluators: two C compilers (GCC and TCC) and one scripting language interpreter (Lua). TCC (tiny C compiler) was written by Fabrice Bellard and was used for the 32 bit version of the algorithm. Unfortunately the compiler does not build on 64 bit targets, therefore the slower C compiler of the GNU Compiler Collection (GCC) was used as fall-back on the 64 bit cluster. The parallel implementation uses MPI (message passing interface) for the communication between nodes. Single-CPU results as well as the test results from the cluster are presented for day trading.

[29] “Backward e forward looking negli schemi payg-ndc”

Working Paper Mefop n. 23/2009, Roma, 2009 (with S. Gronchi)

Abstract. Con l’eccezione di quello italiano (che si distingue anche per una molteplicità di errori) gli schemi a ripartizione di tipo contributivo utilizzano coefficienti di conversione differenziati per coorte: ad ognuna che varca la soglia dell’età pensionabile è assegnato un vettore di coefficienti (differenziati per età al pensionamento) non più modificabile successivamente.

I coefficienti sono di tipo backward looking, cioè il loro calcolo è basato su tavole di sopravvivenza ‘tradizionali’ che, come è noto, riflettono la longevità di tutte le coorti in essere al momento della rilevazione. In presenza di longevità crescente, essi sottovalutano quindi le durate medie (differenti per età al pensionamento) delle rendite di fatto percepite dalla coorte con cui sono assegnati. Tale ‘obsolescenza congenita’ impedisce la realizzazione piena del principio di corrispettività, oltre a generare disavanzi cronici di bilancio. Si sostiene che il problema sarebbe superato dai forward looking, basate su tavole di sopravvivenza che riflettano la reale longevità della coorte cui i coefficienti stessi sono assegnati. Poiché tale longevità diventa esattamente nota solo ex-post (dopo l’esaurimento della coorte) i coefficienti forward richiedono strumenti previsionali la cui attendibilità dovrebbe essere ‘socialmente condivisa’ e sancita dalla legge.

A prescindere da tali rischi di ‘inaccettabilità sociale’ l’articolo dimostra che i coefficienti forward, ancorché in presenza di perfect forsight, producono ‘overshooting’ cioè eccedono in senso opposto. Infatti, tendono a generare avanzi cronici di bilancio pur nel caso che i contributi siano remunerati in base al tasso di crescita della massima salariale.

[28] “The construction of salary lines”

Far East Journal of Applied Mathematics, Volume 34, p. 233-260, ISSN: 0972-0960, 2009

Abstract. The construction of mean salary lines useful to forecast the evolution of working people wages was not enough debated in literature.

Some models useful to the solution of the problem were presented.

In this paper, first some theoretical results on the generalized binomial processes are presented, after models and algorithms useful to construct mean salary lines are given in both cases with constant and with variable promotion probabilities.

[27] “Backward-looking and forward-looking notional-defined-contribution pension schemes”

Journal of Public Finance and Public Choice, Vol. XXVI, N. 2-3, p. 93-108, ISSN: 1120-7019, 2008 (with S. Gronchi)

Abstract. In order to spread notional capital accrued at retirement by members of a cohort over life expectancy, pay-as-you-go notional-defined-contribution (payg-ndc) scheme uses multipliers (different by retirement age) called conversion coefficients. These are backward-looking (b.l.) in that they relay on survival rates observed for previous cohorts in the past. Under increasing longevity, b.l. coefficients undervalue life expectancy, thus preventing full implementation of actuarial fairness (benefits equivalent to contributions)which is the main objective of ndc scheme. They also engender chronic deficits. Forward-looking (f.l.) coefficients, relaying on survival rates forecast for the cohort whom coefficients themselves are assigned to, can improve actuarial fairness. Nevertheless, they face a rather serious political difficulty in that forecasting tools are fallible. This explains why switching to f.l. coefficients is unable to gain social consensus. Abstracting from this, the paper shows that forward-looking coefficients produce ‘overshooting’. In fact, they generate chronic surpluses. The paper also shows that frontloading pension profile helps sustainability because it reduces both surpluses and deficits generated, respectively, by f.l. and b.l. approaches.

[26] “Sostenibilità di lungo periodo del sistema pensionistico pubblico: coefficienti di trasformazione e tasso di sostituzione”

Quaderno anno I numero II/08, Università di Roma Guglielmo Marconi, Roma, 2008

Abstract. Il sistema previdenziale pubblico italiano è stato oggetto di numerose risorse legislative finalizzate a garantirne la sostenibilità finanziaria e sociale messa in crisi da fattori quali il rallentamento economico e l’evoluzione demografica.

In questo lavoro vengono presentate le conseguenze che i recenti interventi normativi (legge 24 dicembre 2007, n. 247) hanno sulla copertura garantita della previdenza pubblica e sul tasso di sostituzione, considerato quest’ultimo indicatore del tenore di vita che potrà essere mantenuto dalle future generazioni al momento del pensionamento.

[25] “SPES: a computational framework for pricing of financial structured product”

International Finance Symposium 2007, Istanbul, 2007 (in collaborazione con R. Gismondi e W. Janko)

Abstract. Platform SPES (Standard Pricing Estimator System) is an efficient and powerful environment to analyze the price complex structured products within the Monte Carlo framework. The platform is implemented in the numerical computing environment MATLAB and the programming language C. The models implemented in SPES allow the user to achieve two targets: to estimate market price (mark-to-market) and to calculate fair values to fulfill regulatory requirements.

Section 2 of this paper provides a short introduction into the use models for equity and interest rate products, the calibration technique and discretization methods for SDE and SSDE.

Section 3 gives an introduction to technical and computational features of the platform.

The MC framework is a very computing intensive technique. In section 4 we will give an introduction to parallel computing, that will be implemented in SPES in the near future.

[24] “Quali pensioni per il domani?”

Rivista AREL – Europa Lavoro Economia, Anno 2007, pp. 27-32 (in collaborazione con S. Gronchi)

Abstract. L’articolo sintetizza i principali risultati di una ricerca che dimostra come l’avvento della formula contributiva, necessaria per garantire stabilmente la sostenibilità del sistema, implicherà coperture pensionistiche assai meno generose rispetto al passato. Dimostra altresì che la caduta tendenziale delle coperture non potrà essere impedita, e neppure significativamente frenata, dall’aggiunta della pensione complementare generata dalla devoluzione del TFR. Piuttosto, l’obiettivo potrà essere in parte raggiunto seguendo un percorso di continui aumenti dell’età pensionabile.

[23] “Quanto è necessario il secondo pilastro?”

La previdenza complementare in Italia, Il Mulino, 2006 (in collaborazione con S. Gronchi)

Abstract. Il saggio affronta due fra le questioni principali che riguardano il futuro del sistema pensionistico italiano: la possibilità che il sistema pensionistico pubblico non fornisca nei prossimi decenni prestazioni di importo adeguato e il ruolo che le pensioni complementari possono svolgere nel sopperire alle eventuali carenze di reddito.

[22] “Un esperimento di capitalizzazione virtuale su due pilastri: la riforma del Fondo Enasarco”

Economia e lavoro, Anno 2005, Volume XXXIX, Fascicolo 2 (Maggio – Agosto), pp. 123-143 (in collaborazione con S. Gronchi)

Abstract. Il lavoro analizza la recente riforma del fondo che eroga, a ripartizione, le pensioni integrative dei rappresentanti di commercio, una categoria importante che conta quasi 220 mila lavoratori autonomi. La formula di calcolo, in precedenza basata sui redditi percepiti nella vita attiva, è stata trasformata lungo le linee previste dalla riforma contributiva che nel 1995 aveva riguardato il primo pilastro. Quest’ultima riforma è stata “importata” piuttosto meccanicamente, cosicché l’occasione è stata persa per riconsiderarne errori ed imperfezioni.

[21] “Appraisal value e modellizzazione stocastica: un percorso obbligato?”

Atti del VI Congresso Nazionale di Scienza e Tecnica delle Assicurazioni, Bologna 18-20 gennaio 2004, Istituto Italiano degli Attuari, 2004

Abstract. L’approccio valutativo di tipo appraisal value mostra una distonia tra l’evoluzione dei contributi scientifici e lo sviluppo della pratica operativa nei mercati internazionali; in particolare nella letteratura di settore, da un tradizionale approccio di tipo classico – deterministico si sono sviluppati contributi verso la modellizzazione stocastica mentre le applicazioni condotte dai principali gruppi assicurativi rimangono ancorate all’approccio tradizionale.
Il lavoro propone alcune soluzioni operative per il passaggio verso l’approccio stocastico alla luce delle view degli operatori del mercato e con pieno riferimento all’evoluzione dei principi IAS.

[20] “Le garanzie nei fondi pensione: un modello di valutazione”

Diritto ed Economia dell’ Assicurazione, Giuffrè Editore, Anno 2004, Volume XLVI, Fascicolo 1, pp. 3-21 (in collaborazione con M. Micocci)

Abstract. Il legislatore italiano ha edificato un sistema di previdenza complementare essenzialmente basato su fondi pensione a contribuzione definita. In realtà, alcuni “nuovi” fondi hanno previsto, per i loro iscritti, prestazioni che contemplano la garanzia di un rendimento minimo indipendentemente dalle effettive dinamiche del benchmark di cui il gestore deve replicare (attivamente o passivamente) le performance. L’inserimento di una siffatta garanzia nello schema pensionistico ha vari effetti: in primo luogo essa aumenta il costo della partecipazione al fondo per l’iscritto; conduce, poi, all’esigenza per il fondo di valutare attentamente la garanzia proposta per far pagare solo il prezzo “equo” all’iscritto per non rischiare da un lato di perdere in competitività sul mercato (cosa che avverrebbe nel caso di prezzo sopravvalutato della copertura), dall’altro di non esporsi al rischio di insolvenza (conseguentemente ad una sottovalutazione della garanzia). Le garanzie di minimo rendimento possono atteggiarsi in vario modo; la versione più intuitiva consiste nel riconoscimento all’iscritto di un rendimento minimo annuale; oppure la garanzia può prevedere la restituzione del capitale (che equivale ad una garanzia di tasso nullo); infine la garanzia potrebbe essere collegata a variabili la cui dinamica futura è incerta (come l’inflazione, l’incremento del TFR, ecc.). In questo lavoro si propone uno schema di valutazione molto flessibile che consente di valutare le garanzie sopra accennate in base alle impostazioni della moderna scienza finanziaria ed attuariale utilizzando cioè la strumentazione tecnica tipica delle assicurazioni sociali e la modellistica della moderna finanza matematica. Nell’articolo sono, inoltre, realizzate alcune applicazioni numeriche.

[19] “La valutazione ex-ante del danno: equità attuariale e decisione razionale”

Atti del XVI Colloquio Biennale Associazione Italiana di Diritto Comparato “Scienza e diritto nel prisma del Diritto Comparato”, Ed. Giappichelli, 2004

Abstract. La trattazione sviluppa un paradigma della scienza (matematica attuariale) e del diritto ove l’argomento è la valutazione del danno, con specifico riferimento all’assicurazione responsabilità civile automobilistica. Viene introdotto il modello decisionale e vengono trattati criticamente i processi metodologici per la determinazione del prezzo equo della copertura assicurativa.

[18] “International accounting standard IAS 19 and the actuarial valuation of termination indemnity funds (TFR Funds) in the Italian firms”

Giornale Istituto Italiano degli Attuari, Anno 2003, Volume LXVI, Fascicolo 1-2, pp. 101-118 (in collaborazione con V. Lovecchio e M. Micocci)

Abstract. L’argomento della valutazione attuariale del Trattamento di fine rapporto secondo il principio contabile internazionale IAS 19 viene analizzato sotto il profilo della criticità dei risultati con riferimento alle basi tecniche utilizzate; l’approccio valutativo è realizzato attraverso il metodo dell’unità di credito proiettata e mediante tecnica simulativa di tipo MAGIS (metodo per anni di gestione e sorteggio individuale).

[17] “Il futuro dell’assicurazione r.c. auto e soluzioni alternative”

Diritto ed economia dell’assicurazione, Giuffrè Editore, Anno 2002, Fascicolo 1, pp. 137-171 (in collaborazione con P. G. Montanari, A. Gambaro e D. Porrini)

Abstract. Il mercato della R.C. Auto è in crisi per ragioni diverse, in parte attribuibili alla natura giuridica della responsabilità civile auto; in parte alle caratteristiche proprie del mercato, quali la liberalizzazione, la crescita del fabbisogno tariffario, l’obbligatorietà della copertura che non consente la selezione del rischio da parte delle Compagnie e l’elevato numero di frodi.

L’articolo analizza le possibili soluzioni per far funzionare meglio l’assicurazione della responsabilità civile auto e per rendere più efficienti le Compagnie assicuratrici,

Se da una parte si suggerisce di modificare l’assetto giuridico della responsabilità civile oggetto di esame, eliminando anche il sistema delle corti di giustizia, tramite l’obbligatorietà di polizze Kasko, dall’altro si intende operare migliorando l’efficienza economica delle Imprese, perseguendo più proficue strategie tariffarie, tramite meccanismi di discriminazione; riducendo la frequenza dei sinistri, tramite interventi legislativi, ed il loro costo medio; isolando i rischi di coda e ponendo un tetto agli indennizzi.

[16] “Valori medi e simulazione per la proiezione degli oneri di un fondo pensioni a prestazione predeterminata”

Giornale Istituto Italiano degli Attuari, Volume LXI, Roma, 1999 (in collaborazione con P. De Angelis)

Abstract. Con riferimento al tema della solvibilità degli schemi previdenziali, viene esaminato l’utilizzo dei metodi analitici e simulativi per la valutazione degli oneri di un fondo pensioni a prestazione definita, fornendo risultati comparativi di specifiche applicazioni al settore.

[15] “Regime fiscale dei fondi pensione in Italia: evoluzione ed analisi del quadro normativo”

Rivista di Politica Economica, ISSN: 0035-6468, Roma, 1998 (in collaborazione con T. Di Gregorio)

Abstract. L’argomento della valutazione dell’impatto fiscale sul finanziamento dei fondi pensione viene affrontato in termini di evoluzione dei contesti normativi di riferimento (ante decreto 124/1993, decreto 124/1993, legge 335/1995); inoltre, con riferimento all’assetto normativo vigente, viene condotta un’analisi quantitativa della convenienza relativa dei fondi pensione come canale di accantonamento di risparmio previdenziale in alternativa ad altri impieghi finanziari.

[14] “Analisi di convenienza all’adesione ad uno schema di previdenza complementare”

Atti Convegno “Aspetti scientifici e didattici nella teoria del rischio”, Università del Molise, Benevento, 1997 (in collaborazione con T. Di Gregorio)

Abstract. Lo studio affronta, nell’ottica del lavoratore, l’analisi di convenienza all’adesione ad uno schema di previdenza complementare in riferimento ad una impostazione metodologica che considera anche, nel caso di versamenti di quote TFR, gli effetti economici derivanti dall’”atteggiamento” dell’impresa.

[13] “Alcune considerazioni sull’evoluzione della tecnica attuariale dei fondi pensione”

Atti Convegno “I Fondi Pensione” Luiss, Roma, 1996

Abstract. Viene esaminato, in ambito matematico-attuariale, il problema delle modalità di versamento dei contributi attraverso l’evoluzione della tecnica attuariale recentemente sviluppatasi sulla tematica in ambito statunitense, evidenziando le caratteristiche e i “rischi” collegati all’utilizzo dei diversi metodi nell’ambito del mercato italiano.

[12] “Sulla determinazione del premio di indifferenza nel rapporto riassicurativo: una applicazione alle forme assicurative in caso di morte”

Dipartimento di Scienze Attuariali e Finanziarie, Nota n. 4, Roma, 1996 (in collaborazione con P. De Angelis)

Abstract. Viene trattato il problema della determinazione del premio di indifferenza nell’ambito di una applicazione alle forme assicurative in caso di morte, secondo i regimi riassicurativi lineari. La sperimentazione dei premi di indifferenza ad un caso aziendale ne evidenzia la qualità e semplicità operativa.

[11] “A Non-Parametric Statistical Model for the control of italian insurance companies”

Rivista A.M.A.S.E.S., Anno 1994, Volume 17, Fascicolo 1 (in collaborazione con P. De Angelis e R. Ottaviani)

Abstract. The problem of evaluating the solvency of insurance companies is tackled through the use of a non-parametric statistical model, constructed using decision-tree techniques. The model is tested on a sample of Italian non-life insurance companies and its performance over the test period compared with those of linear and quadratic parametric models.

[10] “Il problema della ritenzione ottimale dei rischi nel rapporto riassicurativo: un quadro di sintesi tra teoria del rischio e teoria delle decisioni in condizioni di incertezza”

Atti Giornata di Studio su “Il rischio nelle attività delle imprese finanziarie ed assicurative” Università del Molise, Campobasso, 1993 (in collaborazione con P. De Angelis)

Abstract. Nel presente lavoro il problema della determinazione della strategia riassicurativa ottima è inquadrato nell’ambito della teoria delle decisioni in condizioni di incertezza; il ricorso agli schemi formali propri della programmazione matematica consentono un immediato confronto tra teoria classica del rischio e teoria dell’utilità attesa.

[9] “Il problema della ritenzione ottima del rischio con vincolo di offerta: una soluzione operativa nella logica del linguaggio Pascal”

Atti Giornata di Studio su “La valutazione del rischio nella gestione delle imprese finanziarie ed assicurative” Università del Molise, Benevento, 1994 (in collaborazione con P. De Angelis)

Abstract. Nella trattazione il problema di ritenzione ottima del rischio con vincolo di offerta viene formalizzato e risolto nella logica del linguaggio Pascal seguendo l’approccio metodologico fondato sul criterio di individuazione dei vincoli attivi nel punto di stazionarietà della funzione obiettivo.

[8] “Sul problema della ritenzione ottima del rischio con vincolo di offerta”

Atti Giornata di Studio su “La valutazione del rischio nella gestione delle imprese finanziarie ed assicurative” Università del Molise, Benevento, 1994 (in collaborazione con P. De Angelis)

Abstract. L’argomento della ritenzione ottima del rischio è affrontato nell’ambito della teoria delle decisioni in condizioni di incertezza; l’utilizzo delle relazioni a base delle condizioni di equilibrio del mercato consentono di formalizzare il problema di ottimo vincolato con l’esplicitazione di un vincolo esterno di offerta.

[7] “L’approccio bayesiano nella valutazione della solvibilità delle imprese assicuratrici: una applicazione al mercato assicurativo italiano di regole di classificazione fondate su modelli statistici parametrici e non parametrici”

Giornale dell’Istituto Italiano degli Attuari, Anno 1992, Fascicolo 1-2, pp. 43-65 (in collaborazione con P. De Angelis – R. Ottaviani)

Abstract. Il presente lavoro, che si colloca nell’ambito degli studi sviluppati sui modelli statistico-descrittivi per la valutazione di impresa, conclude un programma di ricerca avviato nel 1987 sul settore assicurativo italiano.
Nel lavoro viene fornito uno schema razionale per lo sviluppo di modelli statistici parametrici e non parametrici applicati alle imprese di assicurazione non-vita ed affrontato il problema della misurazione dell’efficienza classificatoria secondo uno schema coerente con l’approccio bayesiano.

[6] “La riforma della previdenza pubblica e lo sviluppo di quella integrativa”

Grifo Banca, Anno 2, n. 5, 1992 (in collaborazione con P. De Angelis)

Abstract. Dopo aver analizzato i principali aspetti quantitativi connessi alla riforma della previdenza pubblica, la trattazione presenta una classificazione delle forme pensionistiche con riferimento alla modalità gestionale e illustra le prospettive di sviluppo della previdenza integrativa.

[5] “Modelli per la valutazione delle imprese assicuratrici: una applicazione al mercato assicurativo italiano di modelli parametrici e non parametrici”

Atti del XVI Convegno A.M.A.S.E.S., Treviso, 1992 (in collaborazione con P. De Angelis – R. Ottaviani)

Abstract. Il lavoro che rientra in un progetto più ampio di ricerca sulle tecniche per la valutazione del rischio d’impresa in campo assicurativo, è quello di fornire, in una ottica comparativa, alcune valutazioni critiche sulla capacità segnaletica di modelli parametrici e non parametrici. In particolare, in una applicazione al mercato assicurativo italiano, è stata proposta un’analisi comparata dell’efficienza classificatoria dei modelli LDA (lineare), QDA (quadratico) e RPA (non parametrico).

[4] “Sulla selezione degli indicatori di bilancio in campo assicurativo”

Atti del XV Convegno A.M.A.S.E.S., Grado, 26-29 settembre 1991

Abstract. Nel presente lavoro sono formulate alcune osservazioni critiche sul processo di selezione delle variabili (indicatori di bilancio) così come è stato affrontato e risolto nei modelli di valutazione del rischio d’impresa definiti in campo assicurativo. Sono state analizzate, da un punto di vista critico, le tecniche più frequentemente utilizzate nella letteratura attuariale ed è stato utilizzato un diverso approccio alla selezione degli indicatori di bilancio.

[3] “Sul rischio finanziario nella teoria attuariale dei fondi pensione”

Nota 16, Dipartimento di Scienze Attuariali e Matematica per le Decisioni Economiche e Finanziarie, Roma, 1990

Abstract. Nel presente lavoro viene analizzato, utilizzando il processo stocastico “flussi di interesse wieneriano”, l’equilibrio attuariale di un fondo pensioni ipotizzando fluttuazioni casuali per il tasso di interesse. L’analisi, svolta nel continuo, rappresenta un contributo ad un approccio stocastico alla teoria attuariale dei fondi pensione.

[2] “Sulla costruzione di un modello non parametrico per la valutazione del rischio d’impresa in campo assicurativo”

Nota 14, Dipartimento di Scienze Attuariali e Matematica per le Decisioni Economiche e Finanziarie, Roma, 1990

Abstract. Il lavoro presenta un modello per la valutazione del rischio d’impresa in campo assicurativo che trova adeguato supporto metodologico nell’ambito delle tecniche non parametriche; il nuovo approccio metodologico evidenzia l’assenza di coefficienti delle variabili (indicatori di bilancio) da stimare facenti parte di una funzione discriminante, tipica dell’approccio valutativo tradizionale.

[1] “Ipotesi per la costruzione di un modello per la valutazione del rischio di impresa in campo assicurativo: un approccio non parametrico”

Atti del 14° Convegno AMASES, Pescara, 1990