Bang-bang control for a class of optimal stochastic control problems with symmetric cost functional. (English) Zbl 1507.93251
Summary: This paper applies the method of backward stochastic differential equations (BSDEs) to study the bang-bang optimal stochastic control problem, where the optimal control is of the feedback form and the final cost functional is given by a symmetric function. In addition to obtaining the existence of the optimal control, we also give the explicit representation of the optimal control and the optimal value function of the stochastic control problem by the explicit solution of nonlinear BSDEs with symmetric terminal condition.
MSC:
| 93E20 | Optimal stochastic control |
| 49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
| 93B52 | Feedback control |
Keywords:
stochastic control; symmetric cost functional; bang-bang control; Girsanov formula; HJB equationReferences:
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