带有随机收益和扰动项的相依风险模型中有限时破产概率的渐近行为

Asymptotic Behavior of the Finite-time Ruin Probability in a Dependent Risk Model with Stochastic Return and Perturbation

本文考虑了一个带有随机收益和扰动项的一般连续时风险模型,其中,投资组合的价格收入过程被描述为几何非负Lévy过程,扰动项是一个实值随机过程,表示保险公司的额外净损失.在理赔额序列满足[J.Korean Statist.Soc.,2012,41(2):213-224]中的相依结构且共同分布是次指数分布的条件下,本文建立了有限时破产概率的渐近估计公式.所得的结果表明,具有次指数理赔额的模型中,有限时破产概率的渐近行为对于该相依结构和轻尾扰动项不敏感.

Consider a general continuous-time risk model with stochastic return and perturbation,in which the price process of the investment portfolio is described as a geometric nonnegative Levy process,and the diffusion perturbation is modelled by a real-valued stochastic process reflecting the additional net loss of an insurer.This paper establishes an asymptotic formula for the finite-time ruin probability under the condition that the subexponential claims follow the dependence structure proposed in[J.Korean Statist.Soc.,2012,41(2):213-224].Our obtained result shows that the asymptotic behavior of the finite-time ruin probability is insensitive to such a dependence structure and the light-tailed perturbation in the risk model with subexponential claims.