引用本文: 程铭, 王定成. 具有随机投资收益过程的风险模型有限时间破产概率的一致渐近估计[J]. 应用概率统计, 2024, 40(4): 558-571.
CHENG M, WANG D C. Uniform asymptotic estimate for the finite-time ruin probability in a risk model with stochastic investment returns [J]. Chinese J Appl Probab Statist, 2024, 40(4): 558−571.
 Citation: CHENG M, WANG D C. Uniform asymptotic estimate for the finite-time ruin probability in a risk model with stochastic investment returns [J]. Chinese J Appl Probab Statist, 2024, 40(4): 558−571.

## Uniform Asymptotic Estimate for the Finite-Time Ruin Probability in a Risk Model with Stochastic Investment Returns

• 摘要: 本文考虑一类利用càdlàg过程刻画保险盈余的随机投资收益, 并利用二元上尾独立刻画保险索赔额之间相依结构的保险风险模型. 一方面, 本文提出条件(6), 在此条件下得到该风险模型有限时间破产概率的一致渐近估计式. 另一方面, 考虑到条件(6)的普适性, 本文发现很多重要的随机过程都满足条件(6), 如Lévy过程, Vasicek模型, Cox-Ingersoll-Ross (CIR)模型和Heston模型.

Abstract: This paper establishes a risk model for an insurer with càdlàg investment returns and heavy-tailed claim sizes which are bivariate upper tail independent. On one hand, we propose condition (6), under which a uniform asymptotic estimate of the finite-time ruin probability in the risk model is obtained. On the other hand, considering the universality of condition (6), we find that the condition (6) can be easily verified by some important stochastic processes, such as the Lévy process, Vasicek model, Cox-Ingersoll-Ross (CIR) model, and Heston model.

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