Section: New Results

Financial Mathematics

Participants : Mireille Bossy, Nicolas Champagnat, Paul Charton, Madalina Deaconu, Dalia Ibrahim, 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 result 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 a clear Nash equilibrium that can be used to compute equilibrium prices on both markets as well as the related electricity produced and CO2 emissions covered [30]

• In addition to the internship of K. Salhi, N. Champagnat, M. Deaconu, and A. Lejay have worked on the use of power law to predict risk in financial markets using data from Euronext NSYE stocks exchanges [33] .

• P. Charton submitted an article [35] on the optimal operation of a windfarm equipped with a storage unit.

Other works in progress

• D. Ibrahim, D. Talay and E. Tanré worked on a model coming from technical analysis in finance. They study the Bollinger Bands indicator to detect jumps in the volatility in an extension of classical Black and Scholes models. They evaluate the efficiency of such indicators to detect the random time at which the volatility jump from a small value to a large one. A paper is being written.

• In collaboration with Victor Reutenauer and Christophe 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 is being submitted.

• In collaboration with J. Bion-Nadal (Ecole Polytechnique and CNRS), D. Talay introduced a new calibration method based on dynamical risk measures and stochastic control PDEs. A paper is being written.