杨龙, 邓国和, 杨立, 黄远敏. 基于广义FGM Copula的相依和扰动风险模型下的Gerber-Shiu函数分析[J]. 应用概率统计, 2019, 35(4): 373-396. DOI: 10.3969/j.issn.1001-4268.2019.04.004
引用本文: 杨龙, 邓国和, 杨立, 黄远敏. 基于广义FGM Copula的相依和扰动风险模型下的Gerber-Shiu函数分析[J]. 应用概率统计, 2019, 35(4): 373-396. DOI: 10.3969/j.issn.1001-4268.2019.04.004
YANG Long, DENG Guohe, YANG Li, HUANG Yuanmin. A Perturbed Risk Model with Dependence Based on a Generalized Farlie-Gumbel-Morgenstern Copula[J]. Chinese Journal of Applied Probability and Statistics, 2019, 35(4): 373-396. DOI: 10.3969/j.issn.1001-4268.2019.04.004
Citation: YANG Long, DENG Guohe, YANG Li, HUANG Yuanmin. A Perturbed Risk Model with Dependence Based on a Generalized Farlie-Gumbel-Morgenstern Copula[J]. Chinese Journal of Applied Probability and Statistics, 2019, 35(4): 373-396. DOI: 10.3969/j.issn.1001-4268.2019.04.004

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

  • 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.

     

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