Study On Some Problems Of Ruin Probability In Insurance Risk Model

Insurance risk theory mainly studies the construction of insurance model and the properties of random variables such as the probability of bankruptcy,the expected discounted penalty function and the discounted value of cumulative dividend payment.In recent years,many scholars have conducted very detailed studies on different insurance risk models.This thesis mainly studies some problems related to bankruptcy probability in different risk models and obtains the properties of the expectation of relevant bankruptcy characteristic quantity.The main research contents of this thesis are as follows:First,we study the linear dividend model update risk process perturbed by diffusion of dividend payments,consider when claims arrival time interval for generalized Erlang(n)distribution of the situation,received before the cumulative dividends discounted the moment generating function and moments of integral differential equation,and gives the claim amount for exponential distribution,explicit expressions of the mean cumulative dividend discount.Finally,the expected discount penalty function in the model is studied and the integral differential equation is obtained.Second,we study the expected discount penalty function in the dual risk model of random observation time.When the time interval is observed as exponential distribution and Erlang(n)distribution respectively,the integral differential equation of the expected discount penalty function is obtained,Then the curve of bankruptcy probability under different distribution is drawn by numerical simulation.Third,we study the insurance risk model with random income with disturbance term and the claim time interval follows the phase distribution,establish the integral differential equation satisfied by the expected discount penalty function.And obtain the Laplace solution of the expected discount penalty function when the amount of income is exponential distribution.