带投资回报的一类期望折现罚金函数

A Class of Expected Discounted Penalty Function with Investment Return

针对时间间隔为相位分布且有两种跳跃方式的连续时间投资回报更新过程。将向上跳表示随机盈利,向下跳表示索赔。在向上跳跃服从指数分布时,向下跳跃有任意的密度函数。首次得到折扣罚金函数满足的积分微分方程,其次通过Laplace变换等计算方法得出了折扣罚金函数的显式表示。

For the phase distribution of time interval and two kinds of jump modes in the continuous time investment return updat-ing process, we make the upward jumps represent random profits and the downward jumps represent claims. Assume that the downwardjumps have an arbitrary density function and the upward jumps have an exponential distribution. At first, we get the integral differentialequation satisfied by the discount penalty function. Secondly, we get the explicit representation of the discount penalty function by La？place transform and other calculation methods.