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On the discrete-time compound renewal risk model with dependence. (English) Zbl 1167.91013
The author studies the discrete-time renewal risk model with dependence between claim amount random variable and the interclaim time random variable.
Two types of dependence structures are considered. The first one uses different bivariate geometric distributions. The second one, more flexible, is based on copulas.
Recursive formulas are derived for the probability mass function, moments and present values of the total claim amount over a fixed period of time.
In the context of ruin theory, some formulas for ruin measures are presented and explicit penalty (Gerber-Shiu) function are derived for special cases.
The author also describes the continuous-time compound renewal risk model with dependence and shows how it can be approximated by the discrete-time model.
Numerical examples are provided to illustrate different topics discussed in the paper.

MSC:
91B30 Risk theory, insurance (MSC2010)
60E05 Probability distributions: general theory
91B70 Stochastic models in economics
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