广义负相依一般风险模型中有限时破产概率的估计及数值模拟

本文研究了一类带利率的重尾相依风险模型, 其中索赔额是一列上广义负相依随机变量, 索赔到达过程是一般的非负整值过程, 并且独立于索赔额序列, 保费收入过程是一个一般的非负非降随机过程. 我们考虑了两种情况, 其一是索赔额、索赔到达过程及保费收入过程相互独立, 其二是累积折现保费收入总量的尾概率可以被索赔额的尾概率高阶控制, 得到了保险公司有限时破产概率的渐近估计,并且给出了相应的数值模拟, 验证了理论结果的合理性.

Estimates and Numerical Simulations for the Finite-Time Ruin Probability in the Extended Negatively Dependent General Risk Model

This paper investigates a dependent heavy-tailed risk model with constant interest rate, where the claim sizes are a sequence of upper extended negatively dependent random variables; the claim arrival process is a general nonnegative integer-valued counting process, which is independent of the claim sizes; and the premium process is a general nonnegative and nondecreasing stochastic process. We obtain an asymptotic result on the finite-time ruin probability of an insurance company in two cases, where, one is the claim sizes, the claim arrival process and the premium process are mutually independent; the other is the tail probability of the total discounted amount of premiums can be highly dominated by that of the claim size. Besides, we conduct some numerical simulations to verify the accuracy of the asymptotic relation in the obtained result.