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MODELLING OF PROBABILISTIC STRUCTURE OF MULTISTATE INSURANCE CONTRACTS (Modelowanie probabilistycznej struktury ubezpieczen wielostanowych)

100%
Debicka J.
Econometrics. Ekonometria. Advances in Applied Data Analytics
|
2011
|
issue 30 (Zastosowania metod ilościowych)
106-120
EN
Multistate insurance is a contract that covers different life accidents. This type of insurances consists of the core insurance contract (usually it is a life insurance) and a package of additional contracts (so called options for example health or disabled insurances). The aim of this paper is to model the probabilistic structure of multistate model. Under the assumption that the stochastic process that describes the evolution of the insurance contract is a non-homogeneous Markov chain, we show how to model the probabilistic structure of multistate model by multiple increment-decrement tables. The obtained results are applied to the analysis of the life insurance with illness and disabled options.
2

PUZZLE OF FINANCIAL MARKET DISTRIBUTION

100%
Stádník B.
Ekonomický časopis (Journal of Economics)
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2014
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vol. 62
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issue 7
709 – 727
EN
In this research we economically explain the observed shape of financial market distributions as this question has still not been fully answered. We suggest the explanation using market price directional dependence which can be also used as an additional one to the nowadays popular volatility dependence solutions. Volatility dependence is based on volatility clustering and does not cover observations of the departures without volatility clusters behind but in this research we also do explain such cases. The whole methodology is based on the financial system internal description therefore we eliminate the internal structure uncertainty which results from just the output/input system description. We try to identify the processes containing the direction dependence within universal model, discuss their contribution to the measured shape of the distributions, make their complex simulation based on the theory of dynamical systems, try to measure them empirically and outline appropriate mathematical description based on Markov chains.
3
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Two-element perturbation of Markov chain in analysis of bonus-malus system

100%
Niemiec M.
Roczniki Kolegium Analiz Ekonomicznych
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2005
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vol. 14
59-74
EN
The purpose of the article is to apply the two-element perturbation of a Markov chain to the analysis of a bonus-malus system commonly employed in automobile insurance in order to classify policyholders. In the literature the bonus-malus system is modelled in the framework of the finite irreducible ergodic discrete Markov chain theory, which requires the assumption of a constant transition matrix and thus restricts the analysis of consequences of changes in the system's structure. In the article the application of the perturbed Markov chain is investigated. The two-element perturbation consists in an increase in one element of the transition matrix at the expense of an equal decrease in one other element in the same raw. In spite of its simplicity the perturbation allows for analyzing structure modification in the bonus-malus system due to specific transition matrix of its model. The perturbation proves to be an adequate tool in the study of consequences of changes in the transition rules i.e. rules determining the transfer of a policyholder from one class to another. It enables to examine the influence of their changes on stationary probabilities, mean first passage and return times and consequently on the system evaluation and performance. Hereby, it provides insurance companies with valuable information, indispensable for constructing a new system or modifying the old one.
4
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Nonhomogeneous Markov chain switching model

100%
Decewicz A.
Roczniki Kolegium Analiz Ekonomicznych
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2005
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vol. 14
143-162
EN
The paper is dedicated to a new approach to analyze changes of qualitative characteristic of economic process by means of a special kind of nonhomogeneous Markov chain basing on the concept of switching models. Qualitative feature of economic process (such as evaluation of economic situation) may be in natural way modeled by polynomial distribution. In the paper the authoress assumes that its distribution is a mixture of multinomial probability distributions with parameters dependent on transition probabilities of a Markov chain. Such approach let treat the data observed as an outcome of a nonhomogeneous Markov chain with transition matrix in each period belonging to a finite set of possible matrices. The choice of the matrix describing the process in each moment of observation is governed by an unobserved regime variable. In other words nonhomogeneity of a Markov chain consists in switches from one regime transition matrix to another. In the paper she develops maximum likelihood estimators of the model's parameters and presents the application of the model to analysis the responses from business tendency survey in Poland for the case of micro data (i.e. when the whole history of responses of each individual respondent is available) and macro data (only the structures of responses are available).
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