一类重尾风险模型的有限时破产概率

Finite-Time Ruin Probability for a Kind of Heavy-Tailed Risk Models

考虑一类随机收取保费的重尾风险模型.与经典的风险模型相比,该模型考虑了保费收取过程的随机性,因而能够更好地刻画保险公司的运营风险.在索赔额服从强次指数分布的条件下,得到了当保险公司的初始资本x趋近于无穷大时,保险公司在时刻t之前破产的有限时破产概率的渐近估计.该渐近结果对于时间t具有一致性.

In this paper, a kind of heavy-tailed risk model with random premium is considered. Compared with that of the classical risk models, in this model, the randomness of the process in the charge for the premium is considered.Therefore, the operation risk of the insurance company can be better characterized. Under the condition that the claim-sizes have a strong subexponential distribution, the asymptotic estimation of the finite-time ruin probability before time t of the insurance company is derived when x, the initial capital of the insurance company tends to be infinity. The asymptotic results have uniformity for the time t.