Section: New Results

Backward stochastic (partial) differential equations with jumps and stochastic control with nonlinear expectation

A. Sulem, M.C. Quenez and R. Dumitrescu have studied optimization problems for BSDEs with jumps [11] , optimal stopping for dynamic risk measures induced by BSDEs with jumps and associated reflected BSDEs. [24] , [80] , [19] . They have also investigated optimal stopping with nonlinear expectation under ambiguity, and their links with nonlinear Hamilton Jacobi Bellman variational inequalities in the Markovian case. Moreover they have obtained dynamic programming principles for mixed optimal-stopping problems with nonlinear expectations. They have also explored the links between generalized Dynkin games and double barriers reflected BSDE with jumps [56] . Stochastic control of Itô-Lévy Processes with applications to finance are studied by A. Sulem and B. Øksendal in [25] , [26] . We have also contributed to the theory of BSDEs and Forward-Backward SDEs which appear as the adjoint equations associated to stochastic maximum principles, and address various issues about the relation between information and performance in non Markovian stochastic control: In particular, in the context of jump-diffusion models under partial information, A. Sulem, C. Fontana and B. Øksendal study in [20] the relation between market viability (in the sense of solvability of portfolio optimization problems) and the existence of a martingale measure given by the marginal utility of terminal wealth, without a-priori assuming no-arbitrage restrictions on the model.

A. Sulem, with B. Øksendal and T. Zhang has studied optimal stopping for Stochastic Partial Differential equations and associated reflected SPDEs [91] , and optimal control of Forward-Backward SDEs [90] .

Stochastic maximum principles for singular mean-field games are obtained in [37] with applications to optimal irreversible investments under uncertainty.

R. Dumitrescu and C. Labart have proposed a numerical approximation for Doubly Reflected BSDEs with Jumps and RCLL obstacles [35] .

R. Elie studies approximate hedging prices under various risk constraints. This is done in collaboration with P. Briand, Y. Hu, A. Matoussi, B. Bouchard, L. Moreau, J.F. Chassagneux, I. Kharroubi and R. Dumitrescu.