基于广义FGM Copula的相依和扰动风险模型下的Gerber-Shiu函数分析
A Perturbed Risk Model with Dependence Based on a Generalized Farlie-Gumbel-Morgenstern Copula
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摘要: 该文考虑了带扰动的相依风险模型,并以一类广义的Farlie-Gumbel-Morgenstern copula定义了索赔额和索赔时间间隔之间的相依结构. 首先, 该模型下期望折扣罚金函数所满足的积分方程、拉普拉斯变换和瑕疵更新方程被给出. 最后当索赔额分布为指数分布时,给出了期望折扣罚金函数所满足的解析解和破产概率的数值实例.Abstract: 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.