Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional

This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional. It involves BSDEs in $L^1$ whose well-posedness is a subtle issue. A suitable framework has been adopted so that the corresponding LQ problem is correctly formulated. Open-loop and closed-loop solvability of such an LQ problem have been investigated and characterized by the solvability of an FBSDE and that of Riccati differential equation.

Source: arXiv:2601.21748v1 - http://arxiv.org/abs/2601.21748v1 PDF: https://arxiv.org/pdf/2601.21748v1 Original Link: http://arxiv.org/abs/2601.21748v1