保险公司在二项风险模型下破产概率的渐进估计

An Asymptotic Estimation for Ruin Probabilities of Insurance Companies with Binomial Risk Model

主要研究完全离散二项风险模型,在条件系数存在的情况下,得到在破产发生的情况下罚金期望所满足的瑕疵离散更新方程及其渐进解,由此得到了保险公司当初始资本为0时破产概率的显示解和当初始资本u→∞时的渐进解和破产时刻所发生的赤字分布当初始资本为0时的显示解和当初始资本u→∞时的渐进解,并在当陪付服从几何分布和赌徒分布的情形下得到了上述特征量的具体结果。

The main risk model we considered in this paper is the fully discrete compound binomial risk model. Under the assumption for the existence of the adjustment coefficent, Firstly,the discrete defective renewal equation, which the expectation of the penalty at the time of ruin is satisfied, and the asymptotic formula of the above expectation are obtained for sufficiently large initial surplus by means of a discrete key renewal limit theorem. Secondly, the exptict expressions for the ruin probability and the probability of the defict at ruin when initial surplus is zero and their asymptotic formulas when initial surplus extends to infinite, i. e. , are derived based on the above results. At last the concrete results of the above problems are obtained under the claim distribution is geometric distribution or the gambler distribution.