Risk Models In The Interest Rate Under The Influence Of A Number Of Issues To Study

The risk theory is the foundation of financial mathematics and the actuarial mathematics of insurance .And the study of the ruin theory is its core. In this paper,we study a class of problems about ruin under interest force. Some expressions or characters of the variables about ruin are obtained.Five chapters are concluded in this whole paper.In the first chapter, we concisely introduce the history, the current situation and the main results of the risk theory. Especially ,we pay more attention to the classical risk model .Finally we present the main content of this paper and the some results of our research.In the second chapter ,we outline the basic knowledge ,such as expectation, point process, martingale,and so on,which is the foundation of this paper.In the third chapter, we discuss the risk model with Markov chain interests. Principally,we study the case of two states. Firstly ,we abtain the equations of the survival probability. Then how to solve the equations is introduced.In the fourth chapter,we consider the classical risk process with return on the investment generating process is a compound Poisson process plus a Brownian motion with positive drift. We obtain the equation of discounted penalty function at ruin.Especially,some quantities, such as ruin probability ,the joint distribution of the surplus before ruinU(T_) and the deficit at ruin U(T),the n th moments of them, and so on,relating the time of ruin ,are obtained when the discounted penalty function at ruin and rate of investment interest are some special functions.In the fifth chapter, we consider the presence of a linear dividend following to the model of the fourth chapter. We derive the equation of the expected value of discounted dividend payments and discounted penalty function at ruin.The sisth chapter is appendix.