一类交错更新风险过程的罚金函数

Penalty Function of a Kind of Alternate Renewal Risk Processes

考虑一类索赔依交错更新过程来到的风险过程,其索赔时间间隔是指数分布与Erlang(2)分布交错持续的随机序列,索赔额是非负独立同分布的随机变量序列.本文给出了罚金函数的拉普拉斯变换,并就指数索赔额分布的情况,推导出了破产概率表达式及其破产前余额与破产时亏损分布的拉普拉斯变换.

A kind of risk processes that have an alternate counting renew process is considered, which means that a claim time interval which has an exponential （or an Erlang（2）） distribution just follows another claim time interval which has an Erlang（2） （or exponential） distribution; the claim amounts are i. i. d. non-negative random variable sequence. In the case of exponential claim amounts, we propose the Laplace transform of the penalty function, an expression of ruin orobabilitv and the Laolace transform of the ioint distribution of surplus before and deficit at ruin.