Kybernetika 62 no. 2, 257-285, 2026

Equilibrium strategies in time-inconsistent stochastic control problems with delayed feedback

Farid Chighoub, Dounia Bahlali and Ayesha SohailDOI: 10.14736/kyb-2026-2-0257

Abstract:

This paper develops a game-theoretic framework for analyzing stochastic differential delayed equations (SDDEs) in time-inconsistent control problems. By extending the Bellman equation to a system of nonlinear equations, the framework identifies subgame-perfect Nash equilibrium strategies for delayed processes with functional objectives. The approach accounts for the challenges introduced by delays and time inconsistency, providing a robust method for deriving equilibrium strategies. To illustrate its applicability, the framework is applied to a mean-variance portfolio selection problem with state-dependent risk aversion and delay, demonstrating how past decisions influence current outcomes. This work advances the theoretical understanding of SDDEs and offers practical insights for applications in finance and related fields.

Keywords:

time inconsistency, equilibrium strategy, extended HJB equations, mean-variance criterion, investment problem with delay

Classification:

93E20, 60H30, 93E99, 60H10

paper.pdf

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