破产时刻罚金折现期望值的更新方程及应用

罚金函数是保险公司破产前瞬间盈余和破产时赤字的函数。在不变利率强度情况下，文献[4]对罚金折现期望作了研究。文献[6]在利率强度带有Posson跳的情况下，对罚金折现期望作了理诉研究，并出了罚金折现期望的更新方程，利用这个更新方程对经典风险理论中一些结果作进一步的讨论。该文在[4],[6]的基础上首先给出[6]中更新方程的另一种简单的概率证明，然后利用Laplace变换和这个更新方程得出了罚金折现期望函数近似计算公式。

The Renewal Equation of the Expected Value of Discounted Penalty at Ruin Time and Its Applications

Penalty function is the function of the deficit at ruin and the surplus immediately before ruin. Expected discounted penalty was discussed in in the case of constant force of interest. In author made a further study on the expectation of discounted penalty and obtained the renewal equation of the expectation of discounted penalty when the force of interest has a Poission jump. Some results in classical risk theory were also discussed by vitue of this equation. Basing on and , in this paper, first we give another simple probabilistic proof of the renewal equation of , then the approximate computational formula of expectation function of discounted penalty is obtained by means of Laplace transforms and the renewal equation.