In 1973,two great financial thcoristcs and practiccrs Fisher Black and Myron Scholes published their famous paper " The Pricing of Options and Corporate Liability " which gave the the Black-Scholes formula,an explicit formula of the pricing of European Option . This is a breakthrough of modern Mathematical Finance .From then on, the research of modern Mathematical Finance gained rapid development with tremendous achievements. Most remarkeable of all,the Black-Scholes model has not only been obtained plentiful results in theoretical rasearch ,but also been applied in financial market broadly. In 1990s the annual transaction volume in global derivative securities market achieved 50,000 billion dollars.In this dissertation,on the basis of the stochastic integral theory of the fractional Brownian Motion,we studied fractional Black-Scholes Model of mathematical finance with arbitrary Hurst parameter are studied systematically and comprehensively .In introduction, we introduced the the history of mathematical finance, espically its main research content, results and hot topics of option pricing theory.In Chapter 2, the definition, properties and its intergal theory of fractional Brownian motion are introduced firstly. Then we gave the definition of quasi-conditional expectation and quasi-martingal, and got the formula of the quasi-conditional expectation for the function of fractional Brownian motion.In Chapter 3, we studied fractional Black-Scholes model, put forward the fractional risk neutral pricing formula by using quasi-coditional expec-tion, then obtained general pricing formulas of European contigent claim at arbitrary time before maturity under different conditions, and also obtained pricing formulas of European options at arbitrary time before maturity under condition that risk-free interest rate and devidends rate were the non-random function of time.In Chapter 4, we introduced several common singular options, under the condition that risk-free interest rate and devidends rate were constant or the non-random function of time ,we obtained the pricing formulas of Bi-... |