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The Maximum Surplus Distribution before Ruin in an Erlang（n） Risk Process Perturbed by Diffusion 被引量：2

The Maximum Surplus Distribution before Ruin in an Erlang（n） Risk Process Perturbed by Diffusion
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摘要 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. 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.
作者 Zhen Zhong ZHANG Jie Zhong ZOU Yuan Yuan LIU
机构地区 College of Science School of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第9期1869-1880,共12页 数学学报（英文版）
基金 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）
关键词 Sparre Anderson risk model generalized Erlang（n） inter-claim times integro-differential equation diffusion process maximum surplus distribution Sparre Anderson risk model, generalized Erlang（n） inter-claim times, integro-differential equation, diffusion process, maximum surplus distribution
分类号 O211.67 [理学—概率论与数理统计] F276.6 [经济管理—企业管理]
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参考文献20

  • 1Dickson, D. C. M., Hipp, C.: Ruin probablities for Erlang(2) risk process. Insurance: Math. Econ., 22, 251-262 (1998).
  • 2Dickson, D. C. M., Hipp, C.: On the time to ruin for Erlang(2) risk process. Insurance: Math. Econ., 29, 333-344 (2001).
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  • 4Dickson, D. C. M., Drekic, S.: The joint distribution of the surplus prior to ruin and the deficit at ruin in some Sparre Andersen models. Insurance: Math. Econ., 34, 97-107 (2004).
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  • 10Sun, L., Yang, H.: On the joint distributions of surplus immediately before ruin and the deficit at ruin for Erlang(2) risk processes. Insurance: Math. Econ., 34, 121-125 (2004).

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Acta Mathematica Sinica,English Series
2011年 第9期

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