This paper is concerned with the stochastic linear-quadratic optimal control problem with Poisson jumps. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed indefinite. The notion of closed-loop strategies is introduced, and the optimal closed-loop strategy is characterized by a Riccati integral-differential equation and a backward stochastic differential equation with Poisson jumps.
Stochastic Linear-Quadratic Optimal Control Problems with Random Coefficients: Closed-Loop Representation of Open-Loop Optimal Controls
General Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems
Direct Method on Stochastic Maximum Principle for Optimization with Recursive Utilities
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