经典风险模型中有限时间区间分红问题

Dividend Problems for Finite Time Interval in the Classical Risk Model

本文研究经典风险模型中有限时间区间分红问题.假设在时间区间[0,t]内,分红按照barrier策略支付,即给定一个非负barrier值b,仅当盈余超过b时,将超过的部分支付分红.利用微分法,得到了[0,t]内期望折现分红(V(x;t))满足的方程,并在指数理赔假设下给出了V(x;t)关于t的Laplace变换的显式表达式.最后,使用Stehfest方法给出一个数值例子.

In this paper, we study the dividend problems for finite time interval in the classical risk model. Assume that the dividends are paid according to a barrier strategy in the time interval [0,t],i.e., given a nonnegative barrier value b, the dividends only can be paid when the surplus exceeds b and the excess is paid as dividend. Applying the "differential argument",the equation for the total expected discounted dividends in the time interval [0,t](V(x;t)) is derived, and the explicit expression for the Laplace transform of V(x;t) with respect to t is obtained under the assumption that the claim sizes are exponentially distributed. Finally, a numerical example is given by Stehfest method.