Search

New algorithms for computing power moments of hitting times and accumulated rewards of hitting type for semi-Markov processes. The algorithms are based on special techniques of sequential phase space reduction and recurrence relations connecting moments of rewards. Applications are discussed as well as possible generalisations of presented results and results of experimental studies., 24 pages

We propose a statistical approach to modelling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modelling the tornado intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornado intensity into six states, it is possible to model the tornado intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reproduce the duration effect that is detected in tornado occurrence. The superiority of the semi-Markov model as compared to the Markov chain model is also affirmed by means of a statistical test of hypothesis. As an application, we compute the expected value and the variance of the costs generated by the tornadoes over a given time interval in a given area. The paper contributes to the literature by demonstrating that semi-Markov models represent an effective tool for physical analysis of tornadoes as well as for the estimation of the economic damages to human things.

The purpose of this paper is to introduce a class of stochastic processes that we call step semi-Markov processes and to illustrate the modelling capacity of such processes in practical applications. The name of this process comes from the fact that we have a semi-Markov process and the transition between two states is done through several steps. We first introduce these models and the main quantities that characterize them. Then, we derive the recursive evolution equations for two-step semi-Markov processes. The interest of using this type of model is illustrated by means of an application in manpower planning.

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., SCOPUS: ar.j, info:eu-repo/semantics/published

In this paper we propose a semi-Markov modulated model of interest rates. We assume that the switching process is a semi-Markov process with finite state space E and the modulated process is a diffusive process. We derive recursive equations for the higher order moments of the discount factor and we describe a Monte Carlo al- gorithm to execute simulations. The results are specialized to classical models as those by Vasicek, Hull and White and CIR with a semi-Markov modulation.

In this article, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

Summary: In this paper, we investigate the impact of the fiscal system on wealth redistribution in Germany, Greece, and Italy. We demonstrate the appli- cation of the model to the data of the quoted countries. We obtain the gross income distributions by starting from the net income distributions downloaded from the Eurostat website and by using the individual income tax rates of each country. We evaluate the Dynamic Theil's Entropy that allows us to recover the total inequality between the net and gross income distributions for each of these countries. Such a comparison allowed us to understand how the fiscal systems affect wealth distribution. These results can be used for planning welfare policies. Income inequality can be measured by means of econometric indices. The most common are the Gini index and Theil's entropy. Henri Theil (1967) introduced Theil's Entropy as an alternative measure of in- come inequality. This index is popular because of its several desirable properties. Of these properties, we use additively decomposability inequality to obtain the values of the indices related to the three European countries of interest. In the whole popula- tion, the Theil's index can be additively decomposed to the inequality between the subgroups and to a weighted average of the inequality within each group. Guglielmo D'Amico and Giuseppe Di Biase (2010) recently generalized Theil's Entropy by taking into account the random time evolution of the agents' in- comes. This led to the formulas for the general dynamic inequality and the concentra- tion indices. In this paper, we investigate the impact of the fiscal system on wealth redistri- bution in the population for each of the considered countries. We could recover the gross income distributions by using the individual income tax rates in these countries over the net income distributions. Then, by following the methodological approach by D'Amico, Di Biase, and Raimondo Manca (2012), we compute the Dynamic Theil's Entropy. Fiscal policy could be a fundamental tool of macroeconomic policy that can decrease income inequality by favoring the redistribution of the wealth.

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.

In this paper we propose a stochastic model to analyze the time evolution of inequality within an economic system. The classical inequality indices, Herfindahl-Hirschman, Gini and Theil’s entropy, are thereby turned into a dynamic form. We show, by using a simulative approach, how it is possible to study the time evolution of inequality in a closed or open economy. We pay particular attention to immigration effects on the inequality. The model is able to manage different behaviors of the inequality indices and it may help decision makers calibrate the economic policies of inequality containment.

In this paper, we present a model to describe the evolution of the yield spread by considering the rating evaluation as the determinant of credit spreads. The underlying rating migration process is assumed to be a non-homogeneous discrete time semi-Markov process. We calculate the total sum of mean basis points paid within any given time interval. From this information we show how it is possible to extract the time evolution of expected interest rates and discount factors.

This paper shows how to apply discrete time non-homogeneous semi-Markov processes (DTNHSMP) with an age index to credit risk. The idea is to consider the credit risk problem as a reliability model indexed by the age and in this way, many semi-Markov results could be adapted to describe credit risk problem. The default state is seen as a "non working state". As the semi-Markov process is a generalization of Markov process, the presented model can be seen as a more general migration model. In fact, in semi-Markov environment the distribution function (d.f.) of the waiting time before a transition can be of any type and without the strong constraints of the Markov model. Furthermore, some results on the asymptotic behavior of the presented model are given. This permits the construction of the d.f. of the default random variable for each "working state". An example, constructed manipulating some Standard & Poor's (S&P) data, is presented.