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