| The Maximum Surplus Distribution before Ruin in an Erlang（n） Risk Process Perturbed by Diffusion |
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| 引用本文： | Zhen Zhong ZHANG,Jie Zhong ZOU,Yuan Yuan LIU. The Maximum Surplus Distribution before Ruin in an Erlang（n） Risk Process Perturbed by Diffusion[J]. 数学学报(英文版), 2011, 27(9): 1869-1880. DOI: 10.1007/s10114-011-8072-8 |
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| 作者姓名： | Zhen Zhong ZHANG Jie Zhong ZOU Yuan Yuan LIU |
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| 作者单位： | [1]College of Science, Donghua University, Shanghai 201620, P. R. China andSchool of Mathematics, Central South University, Changsha 410075, P. R. China [2]School of Mathematics, Central South University, Changsha 410075, P. R. China |
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| 基金项目： | Supported by National Natural Science Foundation of China （Grant Nos. 10901164 and 11071037）, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and Natural Science Foundation of CQ CSTC （Grant No. 2009BB8221） |
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| 摘 要： |
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| 关 键 词： | 风险过程 盈余 分配 扩散 摄动 产前 积分微分方程 边界条件 |
The maximum surplus distribution before ruin in an Erlang(n) risk process perturbed by diffusion |
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| Zhen Zhong Zhang,Jie Zhong Zou,Yuan Yuan Liu. The maximum surplus distribution before ruin in an Erlang(n) risk process perturbed by diffusion[J]. Acta Mathematica Sinica(English Series), 2011, 27(9): 1869-1880. DOI: 10.1007/s10114-011-8072-8 |
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| Authors: | Zhen Zhong Zhang Jie Zhong Zou Yuan Yuan Liu |
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| Affiliation: | 1.College of Science,Donghua University,Shanghai,P. R. China;2.School of Mathematics,Central South University,Changsha,P. R. China |
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| Abstract: | In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang(n) risk process (i.e., convolution of n exponential distributions with possibly different parameters) perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented. |
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| Keywords: | Sparre Anderson risk model generalized Erlang（n） inter-claim times integro-differential equation diffusion process maximum surplus distribution |
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