带干扰的广义Erlang(n)风险模型破产前资产余额的最大值

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.