Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium

Ying Hu (), Hanqing Jin () and Xun Yu Zhou ()
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Ying Hu: IRMAR - Institut de Recherche Mathématique de Rennes - UR - Université de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences Appliquées - ENS Rennes - École normale supérieure - Rennes - UR2 - Université de Rennes 2 - CNRS - Centre National de la Recherche Scientifique - INSTITUT AGRO Agrocampus Ouest - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement
Hanqing Jin: University of Oxford
Xun Yu Zhou: University of Oxford

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Abstract: In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we prove that the explicit equilibrium control constructed in \cite{HJZ} is indeed unique. Our proof is based on the derived equivalent condition for equilibria as well as a stochastic version of the Lebesgue differentiation theorem. Finally, we show that the equilibrium strategy is unique for a mean--variance portfolio selection model in a complete financial market where the risk-free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes.

Keywords: time-inconsistency; mean--variance portfolio selection; stochastic linear-quadratic control; uniqueness of equilibrium control; forward--backward stochastic differential equation (search for similar items in EconPapers)
Date: 2017
Note: View the original document on HAL open archive server: https://hal.science/hal-01139343v2
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Citations: View citations in EconPapers (31)

Published in SIAM Journal on Control and Optimization, 2017, 55 (2), pp.1261-1279. ⟨10.1137/15M1019040⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01139343

DOI: 10.1137/15M1019040

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