Time-Inconsistent Control Theory

Tomas Bjork, Mariana Khapko () and Agatha Murgoci ()
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Mariana Khapko: University of Toronto
Agatha Murgoci: Ørsted

Chapter Chapter 15 in Time-Inconsistent Control Theory with Finance Applications, 2021, pp 147-162 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-3-030-81843-2_15

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