理赔额与理赔间隔相依的风险模型的若干结论(英文)

SOME RESULTS ON A RISK MODEL WITH DEPENDENCE BETWEEN CLAIM SIZES AND CLAIM INTERVALS

本文研究了一类具有相依结构的风险模型.利用无穷小方法,得到了Gerber-Shiu罚金折现期望函数所满足的积分-微分方程,给出了破产时刻,破产赤字及破产前瞬时盈余的拉普拉斯变换的积分-微分方程的应用.最后,在具有常数红利边界下的同一风险模型中,分析了红利支付的期望现值.

In this article, the risk model with a dependent setting is considered. By using differential argument, an integro-differential equation for some Gerber-Shiu discounted penalty functions for the exponentially distributed claim sizes is derived. Applications of the integro- differential equation are given to the Laplace transform of the time of ruin, the deficit at ruin, and the surplus immediately before ruin occurs. Finally, we analyze the expected present value of dividend payments in the same risk model with a constant dividend barrier.