A perturbed risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula. (English) Zbl 1449.62243
Summary: In this paper, we consider a perturbed compound Poisson risk model with dependence, where the dependence structure for the claim size and the inter-claim time is modeled by a generalized Farlie-Gumbel-Morgenstern copula. The integro equations, the Laplace transforms and the defective renewal equations for the Gerber-Shiu functions are obtained. For exponential claims, some explicit expressions are obtained, and some numerical examples for the ruin probabilities are also provided.
MSC:
62P05 | Applications of statistics to actuarial sciences and financial mathematics |
91B05 | Risk models (general) |