带随机干扰更新风险模型破产概率的局部定理

为推广经典风险过程以研究各种风险引发的破产的可能性,本文研究了保险金融领域中一个更为现实的模型:带随机干扰的更新风险模型的破产概率的渐近估计的局部化形式。在相对安全负荷条件下,采用纯概率的方法,得出了当索赔额为重尾索赔时破产概率的局部渐近等价式,它与原更新风险模型相应的破产概率的局部渐近等价式一致,说明在重尾索赔下,Wiener过程对破产概率的影响可以忽略。

A Local Theorem for Ruin Probabilities in the Renewal Risk Model Perturbed by Diffusions

In order to extend the classical risk process to study the possibility of ruin due to various risks, we study the local form of asymptotic estimate for probability in the perturbed renewal risk model which is a more realistic model in insurance and finance. We assume that the relative safety loading condition holds and obtain the asymptotic expression for local ruin probability by using the pure probability method with heavy-tailed claim size, which coincides with that for the corresponding local ruin probability in the renewal risk model. So the influence of the Wiener process can be neglected when the claim size is heavy-tailed.