带观察时的跳服从Erlang(n)分布的对偶模型的红利贴现问题
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引用本文:谈普林.带观察时的跳服从Erlang(n)分布的对偶模型的红利贴现问题[J].经济数学,2015,(3):78-86
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作者单位
谈普林 (武汉大学 数学与统计学院 湖北 武汉430072) 
中文摘要:研究了跳服从Erlang(n)分布,随机观察时服从指数分布的对偶风险模型.假设在边值策略下红利分发只在观察时发生,建立了红利期望贴现函数V(u;b)的微积分方程组.给出了当收益额服从PH(m)分布时V(u;b)的解析解.探讨了当收益额服从指数分布时V(u;b)的具体求解方法.
中文关键词:Erlang(n)分布  红利期望贴现函数  随机观察时  对偶模型  PH(m)分布
 
Dividend Problems in the Erlang(n) Dual Risk Model with Observation Times
Abstract:This paper studied the dual risk model with Erlang(n) distributed inter-claim times and exponentially distributed random observations. Under constant dividend barrier strategy and assumption that dividend payments only occur at observation times, integro-differential equations for expected discounted dividend payments until ruin were established. When jump sizes are PH(m) distributed, the analytical solutions for expected discounted dividend payments were given. When jump sizes are exponentially distributed, the specific method to derive the expected discounted dividend payments was investigated. Specially, the explicit solutions when n=1 and numerical example when n=2 were given.
keywords:Erlang(n) distribution  Expected discounted dividend payments  Random observation  Dual risk model  PH(m) distribution
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