变保费率Cox风险模型的研究

研究了当保费率随理赔强度的变化而变化时C ox风险模型的折现罚金函数,利用后向差分法得到了折现罚金函数所满足的积分方程,进而得到了破产概率,破产前瞬时盈余、破产时赤字的各阶矩所满足的积分方程.最后给出当理赔额服从指数分布,理赔强度为两状态的马氏过程时破产概率的拉普拉斯变换,对一些具体数值计算出了破产概率的表达式.

Study on the Cox Process with Variable Premium

The expected discounted penalty function is investigated under the influence of a premium rate which varies according to the intensity of claims,and the occurrence of claims is described by a Cox process in the considered risk model.By a backward differential argument,we drive the integral equation satisfied by the expected discounted penalty function.Then receive the equations satisfied by ruin probability,the moments of the surplus immediately prior to ruin and the deficit at ruin.Finally get the Laplace transform of ruin probability when the claim size is exponent distribution and claim intensity is two states and the express of ruin probability for exact number.