具有随机收入的一类更新风险模型中的期望折现罚函数

The expected discounted penalty function in a renewal risk model with stochastic income

考虑了具有随机收入的索赔时间间距服从相型分布的保险风险模型.建立了期望折现罚函数所满足的积分方程,当年金收入量为指数分布时,得到了期望折现罚函数的拉普拉斯解.进一步当索赔数量分布属于有理函数族时,给出了期望折现罚函数的解析表达式.

This paper considers the renewal risk model with stochastic income,in which the inter-claim times have phase-type distributions.The integral equation for the expected discounted penalty function is set up.The Laplace transform of the expected discounted penalty function is obtained for exponential premiums.Furthermore,explicit expressions for the expected discounted penalty function are derived when the claim amount distributions belong to the rational family.