MartingaleAnalysis ForTwo Types Of Risk Models With Surrender Factor

Risk theory mainly studies the stochastic risk model in insurance business,which is the basic theory of finance and actuarial Science. As the core problem ofthe risk theory, ruin theory is mostly discussed by many scholars.In insurance, ruin theory not only provides some early risk warning for theinsurance company, but also provides an important theory basis for measuring thefinancial risk that is born by a certain types of insurance company. These years,martingale theory is the hot issue of stochastic process, it is becoming a veryimportant mathematical tool, which has infiltrated into many disciplines. Thenruin probability is derived by martingale method, playing a very importantreferenced value for insurance industry in China.Much of research is based on Poisson risk model and considers constant rate,but general Cox risk model and discrete time risk model are studied poorly,without considering surrender factors and stochastic interest rate.Referring scholars’ research results, the main content as follows:Firstly, martingale theory, the classical risk model and its promotion are led.Secondly, referring the general Cox risk model, this thesis adds stochasticinterest rate, surrender factor and profit from investment. The processes of arrivalof insurance policies, claims and surrender are all considered as Cox process,thus a comprehensive Cox risk model is consist of above all, the upper boundexpression of the ruin probability of the risk model is given by martingalemethod. Assume the rate is zero, without considering surrender factor, the similarresults can be still derived.Thirdly, on basis of the classical discrete time risk model, joining thestochastic interest rate and surrender factor, a new model is composed. Twoexpressions are given on the model of the ruin probability, then the upper bound of ruin probability is calculated by martingale theory. After depredating theclassic to fully discrete time risk model, without considering the stochasticinterest rate and surrender factor, the inequality is also true.