General indefinite backward stochastic linear-quadratic optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 35

A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and the cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in the cost functional are allowed to be indefinite, and the cross-product terms in the control and the state processes are present. Necessary and sufficient conditions for the solvability of the problem are obtained, and a characterization of the optimal control in terms of forward-backward stochastic differential equations is derived. By a Riccati equation approach, a general procedure for constructing optimal controls is developed and the value function is obtained explicitly.

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DOI : 10.1051/cocv/2022030
Classification : 93E20, 49N10, 49N35
Keywords: Backward stochastic differential equation, linear-quadratic, optimal control, Riccati equation, nonhomo-geneous term 
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     title = {General indefinite backward stochastic linear-quadratic optimal control problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2022},
     publisher = {EDP-Sciences},
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Sun, Jingrui; Wen, Jiaqiang; Xiong, Jie. General indefinite backward stochastic linear-quadratic optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 35. doi: 10.1051/cocv/2022030

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