The Compound Poisson Risk Model With Two Dividend Thresholds Strategy And Constant Interest Force

Ruin theory is the core of risk theory,the compound Poisson risk model is always the hotspot area to be studied in ruin theory.Lundberg presented Lundberg-Cramer classical risk model in 1903,then many authors began studying on the model to derive the ruin probability,which can estimate the insurer's solvency.But we can only give an asymptotic estimate or upper bound for the ruin probability in most cases.Later,Gerber etc presented two random variables:the surplus immediately before ruin and the deficit at ruin,then many authors consider the joint and marginal distributions and moments of the surplus immediately before ruin and the deficit at ruin.Recently,Gerber and Shiu (1998)introduced a discounted penalty function with respect to the time of ruin,the surplus immediately before ruin and the deficit at ruin to analyze these related quantities in a unified manner.The Gerber-Shiu expected discounted penalty function has been proven to be a powerful analytical tool.With the development of insurance market and more and more intense competition, the classical risk model has can' t satisfy the requirement of the modern insurance.More and more authors present a series of improvement to the classical risk model.This paper, on one hand,considers the investment income;on the other hand,considers insurant's interest while satisfying insurer's requirement to increase surplus.So we present the compound Poisson risk model with two dividend thresholds strategy and constant interest force.A piecewise nonhomogeneous integral-differential equation is derived for the Gerber-Shiu expected discounted penalty function.We then provide a recursive approach to obtain general solution to the integral-differential equation whenδ= 0.