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Linear-quadratic partially observed forward–backward stochastic differential games and its application in finance

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  • Wu, Zhen
  • Zhuang, Yi

Abstract

This paper is concerned with a partially observed linear-quadratic game problem driven by forward–backward stochastic differential equations where the forward diffusion coefficients do not contain control variables and the control domains are not necessarily convex. The drift term of the observation equation is linear with respect to the state, and there is correlated noise between the state and the observation equation. By virtue of the classical spike variational method and the backward separation technique, we derive a necessary and a sufficient condition of the stochastic differential game problem. Then we obtain filtering equations and present a feedback representation form of the equilibrium point through Riccati equations. As a practical application, we solve a partial information investment problem involving g-expectation as a convex risk measurement and give the numerical simulation to show the explicit investment strategy and illustrate some reasonable phenomena influenced by common financial parameters.

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  • Wu, Zhen & Zhuang, Yi, 2018. "Linear-quadratic partially observed forward–backward stochastic differential games and its application in finance," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 577-592.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:577-592
    DOI: 10.1016/j.amc.2017.11.015
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    References listed on IDEAS

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    1. Huang, Jianhui & Wang, Guangchen & Wu, Zhen, 2010. "Optimal premium policy of an insurance firm: Full and partial information," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 208-215, October.
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    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    5. Bernt Øksendal & Agnès Sulem, 2014. "Forward–Backward Stochastic Differential Games and Stochastic Control under Model Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 22-55, April.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Cited by:

    1. Li, Bo & Huang, Tian, 2024. "Stochastic optimal control and piecewise parameterization and optimization method for inventory control system improvement," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Jiang, Yan & Zhai, Junyong, 2019. "Observer-based stabilization of sector-bounded nonlinear stochastic systems in the presence of intermittent measurements," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 740-752.
    3. Wang, Guangchen & Wang, Wencan & Yan, Zhiguo, 2021. "Linear quadratic control of backward stochastic differential equation with partial information," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    4. Zhang, Shen & Xu, Juanjuan & Zhang, Huanshui, 2024. "Decentralized control of forward and backward stochastic difference system with nested asymmetric information," Applied Mathematics and Computation, Elsevier, vol. 478(C).

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