Stochastic calculus and applications to maths finance

Additional Info

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


    Stochastic calculus is the right mathematical theory for modelling the dynamics of time-continuous financial markets. Prices of assets are expressed as solutions of stochastic differential equations driven by a Brownian motion and wealth of investors as stochastic integrals. Basic hedging methods rely on a neutral-risk description of the underlying financial markets, corresponding to a new of measuring randomness. Students aiming at working in mathematical finance must develop a strong knowledge in stochastic calculus.

  • 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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Home Structure Semester 2 Course units Stochastic calculus and applications to maths finance