The Uniqueness of Equilibrium for Time-Inconsistent Stochastic Linear–Quadratic Control

Ying Hu (1) , Hanqing Jin (2) , Xun Yu Zhou (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 University of Oxford

We prove the uniqueness of an equilibrium solution to a general time-inconsistent LQ control problem under mild conditions which ensure the existence of a solution. This is the first positive result on the uniqueness of the solution to a time inconsistent dynamic decision problem in continuous-time setting. Key words. time-inconsistency, stochastic linear-quadratic control, uniqueness of equilibrium control, forward–backward stochastic differential equation, mean–variance portfolio selection.

Mots clés: time-inconsistency; stochastic linear-quadratic control; uniqueness of equilibrium control; forward--backward stochastic differential equation; mean--variance portfolio selection

Domaines: Gestion de portefeuilles [q-fin.PM]; Probabilités [math.PR]

Ying Hu, Hanqing Jin, Xun Yu Zhou. The Uniqueness of Equilibrium for Time-Inconsistent Stochastic Linear–Quadratic Control. 2015. ⟨hal-01139343v1⟩