Section: New Results

Financial Mathematics

Participants : Mireille Bossy, Nicolas Champagnat, Madalina Deaconu, Antoine Lejay, Khaled Salhi, Denis Talay, Etienne Tanré.

Published works and preprints

  • In collaboration with N. Maïzi (CMA - Mines Paristech) and O. Pourtallier (Coprin team, Inria Sophia Antipolis - Méditerranée), M. Bossy studied the existence of a Nash equilibrium between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. The authors set out the set of Nash equilibria on the electricity market, that constitutes an equivalence class (same prices and market shares) from which they exhibit a dominant strategy. On the coupled markets, given a specific carbon market design (in terms of penalty level and allowances), they compute the bounds of the interval where carbon prices (derived from the previous dominant strategy) evolve. They specify the properties of the associated equilibria (see [30] and [14] ).

  • In their article [40] , N. Champagnat, M. Deaconu, A. Lejay and K. Salhi have constructed a regime switching model for estimating the Value-at-Risk. This model classifies the states in crisis and steady regimes and constructs a mixture of power laws as a model for returns of financial assets.

  • In collaboration with V. Reutenauer and C. Michel (CA-CIB), D. Talay and E. Tanré worked on a model in financial mathematics including bid-ask spread cost. They study the optimal strategy to hedge an interest rate swap that pays a fixed rate against a floating rate. They present a methodology using a stochastic gradient algorithm to optimize strategies. A paper has been submitted [39] .

Other works in progress

  • In collaboration with J. Bion-Nadal (Ecole Polytechnique and CNRS), D. Talay pursued the study of a new calibration methodology based on dynamical risk measures and stochastic control PDEs.