Option Pricing Model And Investment Portfolio Driven By Fractional Brownian Motion

In recent years,along with the quick development of international finance and economics,the place of financial market in social economic becomes more and more important and study of financial derivatives appear increasingly important.Option is an underlying asset. Therefore, whether from the theoretical value or economic sense, it is worth studying.In this paper,we consider the underlying asset in the market driven by fractional Brownian motion,by using stochastic analysis theory and Ito formula,we deduce European option pricing model with transaction cost and bonuses,get the minimum price and analyze the influence of parameters.Finally,we use stochastic analysis theory about fractional Brownian motion to study optimal consumption and portfolio in the market driven by fractional Brownian motion.This paper is divided into five chapters in total.The first chapter is preface and the second chapter is prepare knowledge and fundamental principle,we introduce research background and significance,we also introduce domestic and international research status and some basic theoretical knowledge.In the third chapter, we mainly discuss the fractional Black-Scholes model.By applying no-arbitrage theory,hedging principle and fractional Ito formula,we get the fractional Black-Scholes function and obtain the analytical solution by algebraic transformation.In the fourth chapter, we mainly study the European option with transaction and bonuses drivien by fractional Brownian motion.By applying stochastic analysis theory and hedge principle,we conclude European option pricing formula, show timestep and long-range dependence have a significant impact on option pricing.The fifth chapter mainly deals with the optimal consumption problem in the market driven by the multifractional Brownian motion,introduces a stochastic maximium principle and show the optimal consumption and portfolio.With fractional Brownian motion stochastic analysis theory,we get the optimal solution.