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The Maximum Surplus before Ruin in the Generalized Erlang(n) Risk Model Perturbed by Diffusion
Shanshan Wang *,Chunsheng Zhang
Department of Mathematical Sciences of Nankai University
*Correspondence author
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Funding: 国家自然科学基金,国家自然科学基金（No.2007CB814905,NO. 10871102）
Opened online: 2 February 2009
Accepted by: none
Citation: Shanshan Wang,Chunsheng Zhang.The Maximum Surplus before Ruin in the Generalized Erlang(n) Risk Model Perturbed by Diffusion[OL]. [ 2 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28350
 
 
A maximum surplus before ruin is an important index of assets in insurance institutions. Considering important impact of random error factors on the nature of sample paths of the surplus process, which essentially increases diffculties in research. We investigate the distribution of maximum surplus in generalized Erlang(n) risk model perturbed by diffusion in this paper. We derive a homogeneous integro-differential equation with certain boundary conditions, describing the maximum surplus. Particularly, we can deduce explicit results as long as the individual claim size is rationally distributed. Moreover extending a number of results of simple generalized Erlang(n) risk model(see [7]) successfully, our arguments are more practical and the results are more delicate.
Keywords:Sparre Andersen risk process; Generalized Erlang(n) claim waiting time; Maximum surplus before ruin; Diffusion process; Integro-differential equation
 
 
 

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