On the discrete-time compound renewal risk model with dependence
The author studies the discrete-time renewal risk model with dependence between claim amount random variable and the interclaim time random variable.\newline Two types of dependence structures are considered. The first one uses different bivariate geometric distributions. The second one, more flexible, is based on copulas.\newline Recursive formulas are derived for the probability mass function, moments and present values of the total claim amount over a fixed period of time.\newline In the context of ruin theory, some formulas for ruin measures are presented and explicit penalty (Gerber-Shiu) function are derived for special cases.\newline 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.\newline Numerical examples are provided to illustrate different topics discussed in the paper.
scientific article; zbMATH DE number 5553076
scientific article