常利率下分红双复合Poisson风险模型的期望折现罚金函数

On Expected Discounted Penalty Function for Double Compound Poisson Risk Model with Constant Interest and Dividends

对常利率和常数红利边界策略下的双复合Poisson风险模型进行研究,其中保费收入不再是时间的线性函数,而是一个与理赔过程独立的复合Poisson过程.得到了期望折现罚金函数、破产时的Laplace变换、破产时赤字的期望折现函数以及破产概率满足的积分—微分方程,并借助confluent hypergeometric函数给出指数保费和指数索赔下破产概率的具体表达式.

In this paper,a double compound Poisson risk model has been considered.In contrast with the classical risk model where the premium process is a linear function of time,the aggregate premium process is a compound Poisson process,and it is also independent of the claim process.Moreover,there are a constant interest and a constant dividend barrier strategy in this model.The integro-differential equations for the expected discounted penalty function,the Laplace transform of the time of ruin,the discounted expectation of the deficit at ruin and the ruin probability are derived.Meanwhile,the explicit expression for the ruin probability is given in terms of the confluent hypergeometric functions when the individual stochastic premium amount and claim amount are exponentially distributed.