Section: New Results

Optimal Control of Mean field (S)PDEs

With Rui Chen and R. Dumitrescu, A. Sulem has studied mean-field Backward SDEs driven by a Brownian motion and an independant Poisson random measure and its interpretation in terms of global risk measures. Dual representation has been provided in the convex case. Optimal stopping for these BSDEs and links with reflected mean-field BSDEs has also been investigated.

A. Sulem, R. Dumitrescu and B. Øksendal have studied optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in the case of partial information control [20]. One important novelty is the introduction of general mean-field operators, acting on both the controlled state process and the control process. A sufficient and a necessary maximum principle for this type of control is formulated. Existence and uniqueness of the solution of such general forward and backward mean-field stochastic partial differential equations are proved. These results have been applied to find the explicit optimal control for an optimal harvesting problem.