The Analysis of the Erlang(2) Risk Model with a Two-step Premium Rate

With the gradually maturation and improvement of insurance industry in China,the dividends insurance entered China's insurance market gradually.The policyholder receives not only the compensation which the dividends insurance claims in need,but also the dividend like stock.So the research of payment of dividend is necessary and meaningful.The Gerber-Shiu discounted penalty function of a Erlang(2) risk model with a two-step premium rate that the boundaries of a constant dividend was studied in this paper.By the analysis of the Gerber-Shiu discounted penalty function,the expressions of Gerber-Shiu discounted penalty function and some correlative problems were obtained by using the especial result and common result of the integro-differential equation and some known result.