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Risk processes with dependent claim size and claim occurrence times

100%
Heilpern S.
Śląski Przegląd Statystyczny
|
2012
|
issue 10(16)
57-68
EN
The paper is devoted to the risk process, when the claim amount and the interclaim times may be dependent. The impact of the degree of dependence on the probability of ruin is investigated. The three cases are studied: the case when the joint distribution has the bivariate exponential distribution and when the dependent structure is described by FGM and Clayton copulas. The comparison with the previous study is made too.
2
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Dependent discrete risk processes - calculation of the probability of ruin

88%
HEILPERN S.
Operations Research and Decisions
|
2010
|
vol. 20
|
issue 2
59-76
EN
This paper is devoted to discrete processes of dependent risks. The random variables describing the time between claims can be dependent in such processes, unlike under the classical approach. The ruin problem is investigated and the probably of ruin is computed. The relation between the degree of dependence and the probability of ruin is studied. Three cases are presented. Different methods of characterizing the dependency structure are examined. First, strictly dependent times between claims are investigated. Next, the dependency structure is described using an Archimedean copula or using Markov chains. In the last case, three situations in which the probability of ruin can be exactly computed are presented. Numerical examples in which the claims have a geometric distribution are investigated. A regular relation between the probability of ruin and the degree of dependence is only observed in the Markov chain case.
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