带随机干扰经典风险模型破产概率的局部定理

A Local Theorem for Ruin Probability in the Classical Risk Model Perturbed by Diffusion

研究了带随机干扰的经典风险模型破产概率的局部定理，即假定个体索赔额是重尾分布的前提下得到了破产概率的一个局部等价式R（x，x＋z]～z/ρμ^-F（x），其与Cramér-Lundberg模型中的结果完全一致，其中F表示索赔额的分布函数，μ为其均值，ρ表示模型的安全负荷系数，极限过程是x→β。

This paper is a further investigation into the ruin problem in the classical risk model perturbed by diffusion. Under the assumption that the claims size is heavy-tailed, the authors obtained a local asymptotic relationship for the ruin probability R（x,x＋z]～z/ρμ^-F（x）, which is the same as that in the Cramér-Lundberg model. F denotes the common d.f. of the i. i. d. claims, ρ is the safety loading coefficient of the model, μ is the mean of the claims, and the limit process is x→β.