| Abstract: |
| In this talk we study Pontryagin`s stochastic maximum principle for a mean-field optimal control problem under Peng`s $G$-expectation. The dynamics of the controlled state process is given by a stochastic differential equation driven by a $G$-Brownian motion, whose coefficients depend not only on the control, the controlled state process but also on its law under the $G$-expectation.
Also the associated cost functional is of mean-field type. Under the assumption of a convex control state space we study the stochastic maximum principle, which gives a necessary optimality condition for control processes. Under additional convexity assumptions on the Hamiltonian it is shown that this necessary condition is also a sufficient one. The main difficulty which we have to overcome in our work consists in the differentiation of the $G$-expectation of parameterized random variables.
Based on a joint work with Rainer Buckdahn (UBO, France), Bowen He (SDU, China). |
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