Section: New Results

Financial Mathematics

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

Published works and preprints

• In collaboration with Jerome Lelong and Christophe Deluigi, Sylvain Maire built a new algorithm for the automatic integration and approximation of irregular functions [18] . This algorithm is tested numerically on the pricing of multidimensional exotic options.

• 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 is in revision [55] .

Other works in progress

• K. Salhi works on partial hedging of options in an incomplete market, under constraints on the initial capital of the investor and assuming that the stock price is described by a Lévy process. In this case, perfect hedging is no more possible and we talk about partial hedging and minimization of risk. K. Salhi focuses on the Conditional Value-at-Risk minimization. He tries to give a numerical approximation to the solution in this context.

• 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.