Stochastic Maximum Principle for Fractional Brownian Motion, M.Sc. Thesis Sharif University of Technology ; Zohoori Zangeneh, Bijan (Supervisor) ; Tahmasebi, Mahdieh ($item.subfieldsMap.e)
Abstract
Portfolio optimization is one of the most important issues in capital market and Mathematical Finance. Also in simiulations of financial instruments, in many cases the fluctuations are not independed so we can’t use standard Brownian motion for portfolio optimization and simiulations. In these cases, we should use another kind of Brownian motion which is called fractional Brownian motion. After introducing fractional Brownian motion in chapter 1, we will present its properties in chapter 2 , then at chapter 3 we’ll study stochastic calculus in fractional case and finally in chapter 4 after presenting Stochastic maximum Principle and applying it on a portfolio optimization problem, we will...
Cataloging briefStochastic Maximum Principle for Fractional Brownian Motion, M.Sc. Thesis Sharif University of Technology ; Zohoori Zangeneh, Bijan (Supervisor) ; Tahmasebi, Mahdieh ($item.subfieldsMap.e)
Abstract
Portfolio optimization is one of the most important issues in capital market and Mathematical Finance. Also in simiulations of financial instruments, in many cases the fluctuations are not independed so we can’t use standard Brownian motion for portfolio optimization and simiulations. In these cases, we should use another kind of Brownian motion which is called fractional Brownian motion. After introducing fractional Brownian motion in chapter 1, we will present its properties in chapter 2 , then at chapter 3 we’ll study stochastic calculus in fractional case and finally in chapter 4 after presenting Stochastic maximum Principle and applying it on a portfolio optimization problem, we will...
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