A Class Of Renewal Risk Model

Risk theory studies mainly the stochastic risk model of insurance Actuality. Not only it is a important embranchment of application mathematics in modern,but also a hot topic in the present actuarial science research.By using probability and stochastic processes theory,the classical risk theory studies mainly the surplus process of risk model,ruin time,ruin probability and adjustment coefficient.In order to describe the risk that insurance company being faced with,insurance risk theory is a alteration of the classical risk models.In insurance mathematics,ruin theory is the main contents of insurance risk theory,it supplies a very useful early-warning measure for the risk of the insurance company,it has important theoretical and practical significance.In this dissertation, we get some generalized risk model by extending the claim process.First,the claim process extends the discrete time renewal risk model with constant interest force. Secondly,As a generalization of the classical risk model,a risk model that the claim number is described by Cox process is proposed,in which dependent classes of insurance business coexist.The thesis includes five chapters:The first chapter:Introduces the evolutional course and actuality of risk model,expounded the direction,content and significance of this thesis.The second chapter:Imports the classical risk model and gives a definition of the renewal risk model with constant interest force.The third chapter:This paper is meant to study the discrete time renewal risk model with constant interest force,It mainly discusses the character of the surplus. The expansion of ruin probability and the integral equation of survival probability are proposed,and an estimation of upper bound for the ruin probability is derived by martingale approach.The forth chapter:Imports the Cox model with a constant interest rate and a Cox risk model of double line.The fifth chapter:A risk model that the claim number is described by Cox process is proposed,in which dependent classes of insurance business coexist.The upper boundary of bankruptcy probability is obtained with martingale approach. Through the application of theory of Markov chain,the integral of infinite ruin probability is concluded when the occurrence of the claims follow the mix Poisson process.