The Derivation Of Fractional Fokker-Planck Equation And Its Application In Foreign Exchange Market

In this dissertation, we have got the Fractional Fokker—Planck equation for p (z,t),which is the probability density function of stochastic process {ΔX ( S_α(t))}. At the same time , we have also get the Black--Sholes equation for the option price V ( z,t ) driven by stochastic process {ΔX ( S_α( t))}, the Black--Sholes formular for the option price driven by stochastic process {ΔX ( S_α( t))},which are all not classical.This dissertation is divided into five chapters. In the first chapter, it presents the background and relevant knowledge, such as Fourier (inverse) transformer ,the property ofδ( x). In the second chapter, we mainly introduce how to get the Fokker-Planck equation for f ( x,τ), which is the probability density function of stochastic process {Δx(τ)} . In this chapter , firstly, by applying Laplace transform, then use the definition of transport probability, Fourier transform, the property of functionδ( x), at last we can clearly get the Fokker-Planck equation for f (x,τ). The third chapter is the core of the dissertation, improving the model: (where B (τ)is standard Browian motion, is the price increament for U.S dollar-German mark exchange rates.) The Fractional Fokker—Planck equation for the probability density function of the stochastic process {ΔX ( S_α( t))}can be derived. In the fourth chapter, we mainly considering how to derive the Black-Scholes equation for the option price V ( z,t ) driven by the process {ΔX ( S_α( t))}, the Black-Scholes formular for optional price driven by the process {ΔX ( Sα( t))}, which are not classical. In the last chapter , we present our conclusions, pointing out the direction for our future study.