Stochastic calculus and applications to Math finance

Additional Info

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

     

    This course is devoted to the introduction of the basic concepts of continuous time stochastic processes which are used in many fields : physics, finance, biology, medicine, filtering theory, decision theory. It will consist of a presentation of Brownian motion, Itô integral, stochastic differential equations and Girsanov theorem. Several applications will be given.

  • Topics:

     

    Brownian motion. Filtration and financial information; stopping times. Itô integral, Itô processes and financial strategies. Martingale processes, Girsanov theorem and arbitrage opportunities. Stochastic differential equations and spot prices models. Black-Scholes model.

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