The Ruin Study Of Risk Model With Random Income And Double-Type Insurance Risk Model

In this thesis,in order to much more fit for the practical operation of insurance company,we consider several new models based on the classical risk model.The compound binomial discrete risk model with random income,double-type insurance risk model,and the risk model with thinning process in double-type insurance.We mainly study the expected discounted penalty function,asymptotic estimate,the ultimate ruin probability,the survival probability,the distribution of the surplus prior to ruin, the distribution of deficit at ruin.In chapter one,first,we introduce the situation of insurance and the background of the ruin theory.Second,we introduce the content and the direction of study for ruin theory.Last,we introduce the mainly content of this thesis.In chapter two,under the condition of discrete time,we consider the risk model which the arrival of term policies and the occurrence of claim follow the independent binomial process.We get the recursive formula of the expected discounted penalty function and the asymptotic estimate of the expected discounted penalty function in this model.Then make use of the character of expected discounted penalty function,we get the ruin probability,the distribution of surplus prior to ruin,the distribution of deficit at ruin.A part of this chapter is submitted to Mathematica Applicata.In chapter three,under the condition of continuous time,we consider a continuous time double-type insurance risk model.They have different way to get the premium. One of them follows the function of time t,another is compound Poisson process,and the arrivals of claim also follow Poisson process.The integral representation of the ultimate survival probability,the expression of ruin probability and Lundberg inequality are gotten.This chapter is submitted to Mathematics in Practice and Theory.In chapter four,based on the model of above chapter,we consider the new model,in which the thinning process is considered,using the similar method in chapter three,we get the integral representation of survival probability and so on.This chapter has been published in Guangxi Sciences.