Bankruptcy Time In Several Types Of Risk Model The Expected Present Value Of Its Associated Problems

Since 1998,Gerber and shiu advanced the Gerber-Shiu expected discounted penalty function in the classic risk model.Many scholars discuss the ordinary renewal risk model and the classic risk model perturbed by diffusion. On the basis of these results, In this assertion,we obtain the renewal equation of the expected present value of ruin time in ordinary renewal risk model. Furthermore,we generalize the model to renewal model with diffusion and obtain the renewal equation of the expected present value of ruin time in Erlang(n) risk model with diffusion.In charpter 1: We introduce the risk theory precisely.In charpter 2: We mainly introduce some basic notation and methods which will be useful in the following charpters.In charpter 3: Based on the results of the discounted penalty function,we obtain the renewal function which satisfied by the expected present value of ruin time in ordinary renewal risk model.In addition,according to the relationship of ordinary renewal process and stationary renewal process,we get the the relation of the expected present value of ruin time in them.In charpter 4: We discuss exactly Erlang(n) risk model and obtain its renewal equation of the expected present value of ruin time.And we also get its ruin probability in finite time and the moments of ultimate ruin time.In charpter 5: Furthermore,we generalize the ordinary renewal risk model to the one with diffusion,and obtain the renewal equation of the expected present value of ruin time,the integro-differential equation of the distribution of the maximum surplus before ruin in Erlang(n) risk model with diffusion.