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MATHFI Research team

Financial mathematics

  • Leader : Agnès Sulem
  • Research center(s) : CRI de Paris
  • Field : Applied Mathematics, Computation and Simulation
  • Theme : Stochastic Methods and Models
  • Partner(s) : CNRS,Université Paris-Est Marne-la-Vallée,Ecole des Ponts ParisTech
  • Collaborator(s) : U. PARIS-EST MARNE-LA-VALLÉE (UMLV), CNRS, U. PARIS 12 (CRÉTEIL VAL DE MARNE)

Team presentation

The appearance of increasingly complex financial products requires the use of advanced stochastic and numerical analysis techniques that pose challenging problems for mathematicians. In this field, the scientific skills of the MATHFI research team are focused on the modeling of the price of assets by stochastic processes, probabilistic and determinist numerical methods, stochastic control, with applications to the computation of complex asset prices, dynamic portfolio optimization in incomplete markets, approximate hedging of derivative products and calibration of financial assets.

Research themes

  • Relevant modeling of financial assets (taking into account rare events such as large prices variations, - models with jumps and stable processes, - structural uncertainty concerning the parameters of the statistical dynamics of prices)

  • Numerical methods for pricing and hedging optional products and their implementation
    • Monte-Carlo methods
    • Malliavin calculus
    • Probabilistic numerical methods
    • Study of numerical schemes for parabolic partial differential equations
    • Study of American options : optimal stopping problems
    • Numerical study of Hamilton-Jacobi-Bellman equations

  • Optimization, stochastic control and financial applications
    • Study of realistic hedging techniques (transaction costs, discrete time hedging, constraints on liquid assets)
    • Pricing in incomplete markets.
    • Calibration of financial assets models.
    • Portfolio management.
    • Utility maximisation in incomplete observation.
  • Development of the software Premia for pricing and hedging options and calibration of financial models.

International and industrial relations

  • International collaborations:
    • French-Russian program on financial mathematics of the Liapounov Institute in Moscow; Collaborations with the Department of Mathematics of the University of Oslo, the University of Bath, the Universities of Rome II and III.
    • Teaching in the doctoral programs of Paris and the surrounding region (Paris I, Paris VI, Paris IX, UMLV, University of Evry, Ecole Polytechnique, ENPC).
  • Industrial developments
    • The PREMIA consortium. A consortium of banks is created centered on the PREMIA option computation software. The consortium is currently composed of Caisse des Dépôts et Consignations, the Crédit Industriel et Commercial, the Crédit Agricole/Indosuez, the Crédit-Lyonnais, Natexis-Banques Populaires, EDF, GDF. See website :http://www-rocq.inria.fr/mathfi/Premia/.
    • CIFRE agreementd with EDF (hedging options on electricity), CIC (calibration by Monte-Carlo methods), CAI (interest rate models with stochastic volatility).

Keywords: Sismic