Advanced stochastics and applications to mathematical finance

Additional Info

  • ECTS credits: 6
  • University: University of Nice - Sophia Antipolis
  • Semester: 3
  • Objectives:

     

    This course will focus on the theory of stochastic optimal control and its applications in mathematical finance. The lectures will address both time discrete and time continuous models. A special care will be paid to the derivation of the dynamic programming principle and to the analysis of the corresponding Hamilton-Jacobi-Bellman equations. Typical examples of applications will include optimal allocation problems, based on Morgensten and Von Neumann utility functions, and optimal

  • Topics:

     

    Stochastic control. Dynamic programming principle; Hamilton-Jacobi-Bellman equations. Optimal allocation problem; Utility functions and mean-variance criterion. Optimal stopping; American options. Cox-Ross-Rubinstein and Black Scholes models.

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