Stochastic calculus and applications to maths finance
Additional Info
- ECTS credits: 6
- Semester: 3
- University: University of Nice - Sophia Antipolis
- Lecturer 1: C. Bernardin
- Lecturer 2: R. Catellier
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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.
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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.
