"Probability & Finance" section of the Université Pierre & Marie Curie (Paris 6)

(Directors: N. El Karoui - G. Pagès - M. Yor)

**OBJECTIVES**

(Directors: N. El Karoui - G. Pagès - M. Yor)

The aim of the "Probability & Finance" section of the DEA "Probability & Applications" is to provide high level courses in Mathematical Finance. It is focused on Mathematical investment Finance, with two main topics: derivative securities and the modelling of interest rates.

We supply the mathematical tools which are necessary to handle the increasing complexity and technical nature of the financial markets: stochastic calculus (for Ito and Levy processes), numerical probability, and statistics. During the first semester, students must attend 6 courses in mathematics covering the above fields, 3 courses in finance and 2 optional "advanced" courses from the list below.

The second semester (from April to September) is devoted to an internship (training course) in either a bank, a financial institution or an insurance company.

More information can be found on our web site http://deafinance.proba.jussieu.fr

**Upgrading Courses (Pre-registration obligatory)**

The optional courses proposed below may change every year. They follow the recent developments in mathematical finance, as well as new problems arising within the markets. They are set to commence in February and March.

**J. G. ATTALI**: Asset allocation and multi-asset arbitrage. (15 hours of classes, 3 ECTS)**Ch. AVENE**: Risk Theory within the Insurance Sector/Market (15 hours of classes, 3 ECTS)**O. BARDOU**: Risk management and Evalution with the energy markets (15 hours of classes, 3ECTS)**J. BERTOIN**: Lévy Process (15 hours of classes, 3 ECTS).**P. GARAMPON**: Financial Risk management (15h, 3ECTS)**C. A. LEHALLE**: Quantitative trading: using high frequency estimators for execution and arbitrage. (15 hours of classes, 3 ECTS)**G. PAGÈS**: American Options: Theory and Numerical and Methods (15 hours of classes, 3 ECTS)**H. PHAM**: Stochastic Control and Portfolio Management (15 hours of classes, 3 ECTS)**O. PIRONNEAU**: New stochastic and deterministic numerical tools for option pricing (15 hours of classes, 3 ECTS)**D. TALAY**: Probabilistic analysis of boundary conditions for parabolic or elliptic partial differential equations. (15h, 3ECTS)**N. TOUZI**: Probability Methods for PDEs and Financial Applications (Applications within the financial sector/market) (15 hours of classes, 3ECTS)**S. CHOUKROUN**: Blockchains : from the launch of Bitcoin to today. Fintechs : presentations and opportunities (15 hours of classes)**J. TURC, D. BENHAMOU**: Quantitative Strategies: Applied to the Credit market (15 hours of classes, 3ECTS)**J. JACOD**: Elements of discontinuous stochastic calculus

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