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This paper is concerned with the stochastic linear-quadratic optimal controlproblem with Poisson jumps. The coefficients in the state equation and theweighting matrices in the cost functional are all deterministic but are allowedindefinite. The notion of closed-loop strategies is introduced, and the optimalclosed-loop strategy is characterized by a Riccati integral-differentialequation and a backward stochastic differential equation with Poisson jumps.

Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps