有界风险模型中Gerber-Shiu函数的若干结果  

Some Results of Gerber-Shiu Discounted Penalty Function in the Risk Model with a Constant Dividend Barrier

作　　者：张未未[1] 

机构地区：[1]惠州学院数学系,广东惠州516015

出　　处：《绍兴文理学院学报》2007年第7期1-6,共6页Journal of Shaoxing University

基　　金：国家自然基金(79970022);航空基金(02J53079)资助.

摘　　要：研究了有界风险模型中的Gerber-Shiu函数,得到了当索赔到达Erlang(2)过程时Gerber-Shiu函数满足的微积分方程,并进行求解.进而研究了延迟更新有界风险模型中,对首次索赔时刻的分布加入一个新的参数时Gerber-Shiu函数的变化,并得到了一个数学上易处理的Gerber-Shiu函数的公式.The Gerber- Shiu discounted penalty function is further considered for the risk model with a constant dividend barrier. An intergro- differential equation is derived and solved for the claim occurrence relating to Erlang（2） process. A mathematically tractable formula is derived for the Gerber- Shiu function in the situation where a new parameter is introduced in the time distribution for the first claim for a class of delayed renewal risk processes with barrier.

关 键 词：‰er—Shiu函数 平稳更新风险过程 LAPLACE变换 破产时刻 破产赤字 破产前瞬间盈余 

分 类 号：O29[理学—应用数学] F224.7[理学—数学]