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Optimization Under Rational Expectations: A Framework of Fully Coupled Forward-Backward Stochastic Linear Quadratic Systems

Author

Listed:
  • Mingshang Hu

    (Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, Shandong 250100, People’s Republic of China)

  • Shaolin Ji

    (Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, Shandong 250100, People’s Republic of China)

  • Xiaole Xue

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

Abstract

In this paper, we propose a general modeling framework for optimal control of stochastic fully coupled forward-backward linear quadratic (FBLQ) problems with indefinite control weight costs that stem from rational expectations models. We propose a new decoupling technique to obtain the optimal feedback control, which is accompanied by one kind of non-Riccati-type ordinary differential equation (ODE). By applying the completion-of-squares method, we prove the existence of the solutions for the obtained ODEs. The obtained results make it possible to compute the control and value function. For this FBLQ problem, the optimal control should depend on the entire trajectory of the state process. Several examples are given to illustrate our results.

Suggested Citation

  • Mingshang Hu & Shaolin Ji & Xiaole Xue, 2023. "Optimization Under Rational Expectations: A Framework of Fully Coupled Forward-Backward Stochastic Linear Quadratic Systems," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1767-1790, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1767-1790
    DOI: 10.1287/moor.2022.1319
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