保费随机的离散风险模型的罚金期望函数(英文)

The Expected Discounted Penalty Function at Ruin of the Discrete Risk Model with Random Income

本文把经典的复合二项风险模型进行推广,其中保费收取方式不再是时间的线性函数而是一个二项过程.我们把它的罚金期望看成初始资本的函数,得到了罚金期望函数的递推公式和渐近估计,最后利用罚金期望函数的递推公式和渐近估计给出了几个重要的破产量的递推公式及其渐近估计.

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process,is no longer a linear function. We examine the expected discounted value of a penalty at ruin, which is considered as a function of the initial surplus. A mathematically recursive formula is derived for the expected discounted penalty function, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give some examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.