随机观察时间对偶风险模型中的期望折现罚函数

The expected discounted penalty function in the dual insurance risk model with randomized observation periods

考虑了复合Poisson风险过程的对偶模型,当观察时间间距分别为指数分布和Erlang(n)分布时,得到了期望折现罚函数的积分-微分方程.假设随机收入服从指数分布情形时,给出了期望折现罚函数的解析表达式.最后进行了数值模拟.

The dual model of the compound Poisson risk process with the exponential distributed and Erlang(n)distributed interval of time between two successive observations is considered,respectively.The integro-differential equation satisfied by the expected discounted penalty function is derived.The explicit expression if the stochastic sudden gain follows an exponential distribution is given.Numerical examples are presented.