Optimal control of mean-field jump-diffusion systems with noisy memory. (English) Zbl 1417.49025
Summary: This paper is concerned with an optimal control problem under mean-field jump-diffusion systems with delay and noisy memory. First, we derive necessary and sufficient maximum principles using Malliavin calculus technique. Meanwhile, we introduce a new mean-field backward stochastic differential equation as the adjoint equation which involves not only partial derivatives of the Hamiltonian function but also their Malliavin derivatives. Then, applying a reduction of the noisy memory dynamics to a two-dimensional discrete delay optimal control problem, we establish the second set of necessary and sufficient maximum principles under partial information. Moreover, a natural link between the above two approaches is established via the adjoint equations. Finally, we apply our theoretical results to study a mean-field linear-quadratic optimal control problem.
MSC:
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49N10 | Linear-quadratic optimal control problems |
References:
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