Volume 27, 2021
|Number of page(s)||27|
|Published online||26 May 2021|
Linear-quadratic optimal control for backward stochastic differential equations with random coefficients
Department of Mathematics, Southern University of Science and Technology,
518055, PR China.
2 Department of Mathematics, National University of Singapore, Singapore 119076, Singapore.
*** Corresponding author: email@example.com
Accepted: 3 May 2021
This paper is concerned with a linear-quadratic (LQ, for short) optimal control problem for backward stochastic differential equations (BSDEs, for short), where the coefficients of the backward control system and the weighting matrices in the cost functional are allowed to be random. By a variational method, the optimality system, which is a coupled linear forward-backward stochastic differential equation (FBSDE, for short), is derived, and by a Hilbert space method, the unique solvability of the optimality system is obtained. In order to construct the optimal control, a new stochastic Riccati-type equation is introduced. It is proved that an adapted solution (possibly non-unique) to the Riccati equation exists and decouples the optimality system. With this solution, the optimal control is obtained in an explicit way.
Mathematics Subject Classification: 93E20 / 49N10 / 60H10
Key words: Linear-quadratic optimal control / backward stochastic differential equation / random coefficient / stochastic Riccati equation
© EDP Sciences, SMAI 2021
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