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 5 in Time-Inconsistent Control Theory with Finance Applications, 2021, pp 41-56 from Springer

Abstract: Abstract We now go on to study a class of time-inconsistent control problems. Before proceeding to the formal theory, we first recall a part of our discussion on the Bellman optimality principle from the Introduction. We then detail the game-theoretic formulation, whereby we view the problem as a non-cooperative game with one player at each point in time representing different incarnations of decision maker’s preferences. The main result of this chapter is the extension of the standard Bellman equation, in the form of a system of nonlinear equations, for the determination of the equilibrium strategy and the equilibrium value function. We arrive at the extended Bellman system by first studying a couple of simpler problems to highlight the main ideas and then by bringing things together for the general case.

Date: 2021
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DOI: 10.1007/978-3-030-81843-2_5

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