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An Application of Stochastic Optimal Control in Solving the Mean-variance Portfolio Selection Problem

Tabatabaee Habib abadi, Fattaneh | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44611 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Farhadi, Hamidreza
  7. Abstract:
  8. In this essay, by putting in the framework of linear-quadratic optimal control (LQ),we study and solve the mean-variance portfolio selection problem. Two models will be studied in our work; in one we assume that the price process satisfies a diffusion stochastic differential equation, while in the second model, we assume it to satisfy a jump-diffusion stochastic differential equation. In both models, a formula for the efficient frontier is obtained. This essay is mainly obtained from the works of the following articles and books:
    1)X.Y. Zhou and D. Li, Continuous-Time Mean-Variance Portfolio Selection:A Stochastic LQ Framework. Applied Mathematics and Optimization. 42(2000), 19–33.
    2)T.Liu,J.ZhaoandP.Zhao,PortfolioProblemsBasedonJump-DiffusionMod- els. Filomat. Vol. 26, No 3 (2012), 573–583.
    3)J. Yong and X.Y Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York, 1999.
    4)W.H. Fleming and H.M. Soner, Controlled Markov Processes and ViscositySolutions. Springer-Verlag, 1993
  9. Keywords:
  10. Mean-Variance Method ; Portfolio ; Efficient Frontier ; Stochastic Linear Quadratic Control ; Jump-Diffusion Model