Options Game Approach In Insurance Pricing

As one of the important parts of insurance, pricing problem has been studied for many years.Up to now, the main methods of insurance pricing includes:actuarial pricing approach, option pricing approach, backward stochastic differential equation approach and options game approach. In recent years, options game model takes insurance as an option, using the option game approach to get the optimum premium.In this paper,we use the method of option game to analyze insurance pricing problem.The arrangements of the paper are as follows:The first part introduces the background of the subject, the development process of insurance pricing theory at home and abroad, and the research idea of the paper.The second section of the paper discusses the mathematical methods of insurance pricing after some information about insurance.First in the aspect of actuarial,it gives net premium principle, expectation theory and zero utility theory, followed by some comparations beween them. Another mathematical method is backward stochastic differential equations.The model based on this theory can give a formulation of insurance pricing which is a useful method to solve the insurance pricing problem in an incomplete market.In the third part,we discuss the insurance option model and insurance game model. Through takes insurance as option,we extend the important CAPM and B-S option pricing model to the insurance option pricing model. In the following,we apply the information of game to insurance pricing, and established the basic pricing model of the insurance game.The fourth part uses the option game approach to study insurance pricing problem which can be seen as an American put option.First it establises a B-S equation whose boundary condition with a letter a and a compensaion S.Then through the solution of the B-S equation and the game theory,we can get the fair premium.The fifth presents a summary and further improvement of the paper.