We prove a stochastic maximum principle for a control problem where the state equation is delayed both in the state and in the control, and both the running and the final cost functionals may depend on the past trajec-tories. The adjoint equation turns out to be a new form of linear anticipated backward stochastic differential equations (ABSDEs in the following), and we prove a direct formula to solve these equations.
Guatteri, G., Masiero, F. (2021). Stochastic maximum principle for problems with delay with dependence on the past through general measures. MATHEMATICAL CONTROL AND RELATED FIELDS, 11(4 (December 2021)), 829-855 [10.3934/mcrf.2020048].
Stochastic maximum principle for problems with delay with dependence on the past through general measures
Masiero, Federica
2021
Abstract
We prove a stochastic maximum principle for a control problem where the state equation is delayed both in the state and in the control, and both the running and the final cost functionals may depend on the past trajec-tories. The adjoint equation turns out to be a new form of linear anticipated backward stochastic differential equations (ABSDEs in the following), and we prove a direct formula to solve these equations.
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