The Dividend Problem Of The Erlang(2) Model With Constant Interest And Brownian Motion

The research on the risk theory was the classical risk model initially, then people began considering the influence under destabilization, interest rates and other factors on the classical risk model, but as the ideal of the classical risk model, taking into account the influence of the actual environment, people began to study the models which are more closer to the real life, such as:the renewal risk process,the dual risk model, the dependent risk model, two-dimensional risk model and so on.In this passage, we mainly analyze the problem of dividend about the Erlang(2) model with Brownian motion and interest. In insurance risk model, we often think over two dividend strategies:one is barrier strategy, and another is threshold strategy. Under the barrier strategy, no dividend is paid when the surplus is below a constant dividend barrier b(b>0), and all of the surplus above b is paid out as dividends; Under the threshold strategy, no dividend is paid when the surplus is below a certain barrier level b(b>0), and dividends are paid at a rate α(a>0). We also consider the problem of dividend in the Erlang(2) model under the two dividend strategies.’Firstly, we derive the Integro-Differential equations which the moment generating function M(u, y; b) satisfies, then via the relationship of the moment generating function M(u, y; b) and the mth moment of the dividend function Vm(u, b):In this paper, we derive the Integro-Differential equations which the dividend func-tion: in the Erlang(2) model with Brownian motion and interest satisfies as follows:0≤u<b, This paper is structured as follows:Chapter1is introduction, we mainly describe the history and development of the risk process, the achievements about the insurance risk theory which the domestic and foreign experts have finished, the model and the definition of each quantity in the context are given in the introduction. In Chapter2, firstly we derive a conclusion in the classi-cal model then we mainly research the Integro-Differential equations which the moment generating function of the model satisfies. In Chapter3, through the relationship of the moment generate function and dividend function we study the Integro-Differential equa-tion which the dividend function V(u,b) satisfies. In Chapter4, we mainly discuss the Integro-Differential equations of the Gerber-Shiu function and the Laplace transformation satisfy. In Chapter5, we chiefly give the specific examples for the dividend function.Since the Integral-Differential equations we derived in this paper are variable coeffi-cient differential equations, it is difficult to solve these equations, this is the problem we need to solve and improve in this model, and it is also a defect in this paper.