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

Mingshang Hu (), Shaolin Ji () and Xiaole Xue ()
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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

Mathematics of Operations Research, 2023, vol. 48, issue 3, 1767-1790

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.

Keywords: Primary: 93E20; secondary: 60H10; 35K15; fully coupled forward-backward stochastic differential equation; linear quadratic optimization control; stochastic maximum principle; completion-of-squares method (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:3:p:1767-1790

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