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.
The project was supported by the National Natural Science Foundation of China (Grant Nos. \!11461008; 11761014), the Guangxi Natural Science foundation (Grant Nos. 2016GXNSFBA380035; 2017GXNSFAA198243; 2018GXNSFAA281016), Open Foundation for Key Laboratories and Statistical Models in Universities of Guangxi (Grant No. 2017GXKLMS002) and the Youth science Foundation of Guangxi Normal University (The study of ruin problems based on dependent risk models).
YANG Long,DENG Guohe,YANG Li��. A Perturbed Risk Model with Dependence Based on a Generalized Farlie-Gumbel-Morgenstern Copula[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2019, 35(4): 373-396.