Section: New Results

Stochastic control

Participants : Frédéric Bonnans, Xiaolu Tan [CMAP] , Imene Ben Latifa, Mohamed Mnif [ENIT, Tunis] .

In [24] , we extend a study by Carmona and Touzi on an optimal multiple stopping time problem in a market where the price process is continuous. In this paper, we generalize their results when the price process is allowed to jump. Also, we generalize the problem associated to the valuation of swing options to the context of jump diffusion processes. Then we relate our problem to a sequence of ordinary stopping time problems. We characterize the value function of each ordinary stopping time problem as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman Variational Inequality.

In [27] , we consider, in the framework of Galichon, Henry-Labordère and Touzi, the model-free no-arbitrage bound of variance option given the marginal distributions of the underlying asset. We first make some approximations which restrict the computation on a bounded domain. Then we propose a gradient projection algorithm together with a finite difference scheme to approximate the bound. The general convergence result is obtained. We also provide a numerical example on the variance swap option.