Stochastic Maximum Principle for Fractional Brownian Motion

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Jamshidi, Mohammad Hadi | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50130 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohoori Zangeneh, Bijan; Tahmasebi, Mahdieh
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 take quick review on fractional stochastic differential equations
Keywords:
Fractional Brownian Motion ; Stochastic Optimization ; Maximum Principle ; Stochastic Differential Equation ; Mathematical Finance

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