Explicit　Expressions　for　the　Ruin　Probabilities　of　Erlang　Risk　Processes　with　Pareto　Individual　Claim　Distributions

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	Explicit　Expressions　for　the　Ruin　Probabilities　of　Erlang　Risk　Processes　with　Pareto　Individual　Claim　Distributions
其他题名	Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with Pareto Individual Claim Distributions
	Wei Li 1; Yang Hailiang 2
	2004
发表期刊	应用数学学报：英文版
ISSN	0168-9673
卷号	20.0 期号:003 页码:495-506
摘要	In this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of u when the claim size follows a Pareto distribution. Follow Ramsay, Laplace transforms and exponential integrals are used to derive the solution, which involves a single integral of real valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are given to illustrate the main results.
其他摘要	In this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of u when the claim size follows a Pareto distribution. Follow Ramsay8
关键词	破产可能性 Erlang解法排列分布拉普拉斯变换康托集实变函数
收录类别	CSCD
语种	中文
CSCD记录号	CSCD:1613708
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/53766
专题	中国科学院数学与系统科学研究院
作者单位	1.中国科学院数学与系统科学研究院 2.香港大学
推荐引用方式 GB/T 7714	Wei Li,Yang Hailiang. Explicit　Expressions　for　the　Ruin　Probabilities　of　Erlang　Risk　Processes　with　Pareto　Individual　Claim　Distributions[J]. 应用数学学报：英文版,2004,20.0(003):495-506.
APA	Wei Li,&Yang Hailiang.(2004).Explicit　Expressions　for　the　Ruin　Probabilities　of　Erlang　Risk　Processes　with　Pareto　Individual　Claim　Distributions.应用数学学报：英文版,20.0(003),495-506.
MLA	Wei Li,et al."Explicit　Expressions　for　the　Ruin　Probabilities　of　Erlang　Risk　Processes　with　Pareto　Individual　Claim　Distributions".应用数学学报：英文版 20.0.003(2004):495-506.