Option Pricing Problem In Fuzzy Environment

Option pricing is one of the key problems in modern financial.Black and Scholes hypothesized that stock price fluctuations conform to geometric Brownian motion,and then established stochastic financial mathematics.However,financial uncertain factors are not only random but also fuzzy,thus it is necessary to study the fuzzy financial market.Liu process is an important tool to deal with option pricing in fuzzy financial market.The object of this paper is to make option pricing in fuzzy environment.Based on fuzzy number and fuzzy set theory,the result of studying option pricing by using fuzzy objective function is still a fuzzy number.However,in the the from work of credibility theory,by using the method of expectation.Assuming that the price of the underlying asset follows a Liu process,the expected exact value of the option price can be obtained from the portfolio based on this process,then investors can make better decisions.On the basis of credibility theory and Liu process,this paper establishes several kinds of fuzzy portfolio selection models,and derives corresponding option pricing formulas by using expectation method and insurance actuarial.The main contents are as follows:1.Assuming that the stock price conforms to Geometric fractional Liu process,a pricing model of stock option under periodic dividend payment is proposed,the pricing formula is derived,and a numerical example is given.2.A stock option pricing model with diffusion process is proposed,the pricing formula is deduced,and a numerical example is given.3.Apply the insurance actuarial to price the American disaster insurance futures option in fuzzy environment and derive the pricing formula.4.Apply the insurance actuarial to price foreign exchange options in fuzzy environment and derive the pricing formula.