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

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  • Zixuan Li

    (School of Mathematics, Shandong University, Jinan 250100, China)

  • Jingtao Shi

    (School of Mathematics, Shandong University, Jinan 250100, China)

Abstract

The stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefinite. The notion of closed-loop strategies is introduced, and the sufficient and necessary conditions for the closed-loop solvability are given. The optimal closed-loop strategy is characterized by a Riccati integral–differential equation and a backward stochastic differential equation with Poisson jumps. A simple example is given to demonstrate the effectiveness of the main result.

Suggested Citation

  • Zixuan Li & Jingtao Shi, 2022. "Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps," Mathematics, MDPI, vol. 10(21), pages 1-25, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4062-:d:959899
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    References listed on IDEAS

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    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Sun, Jingrui & Yong, Jiongmin, 2019. "Linear–quadratic stochastic two-person nonzero-sum differential games: Open-loop and closed-loop Nash equilibria," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 381-418.
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