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Erschienen in:
2021 | OriginalPaper | Buchkapitel
15. Time-Inconsistent Control Theory
verfasst von : Tomas Björk, Mariana Khapko, Agatha Murgoci
Erschienen in: Time-Inconsistent Control Theory with Finance Applications
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Abstract
We now move on to study time-inconsistent control problems in continuous time and, as in Part II, we use a game-theoretic framework, studying subgame-perfect Nash equilibrium strategies. It turns out, however, that the equilibrium concept in continuous time is quite delicate and so requires a detailed investigation. Our main result is an extension of the standard HJB equation to a system of equations: the extended HJB system. We also prove a verification theorem, showing that a solution to the extended HJB system does indeed deliver the equilibrium control and equilibrium value function for our original problem.