On time-inconsistent stochastic control in continuous time

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

Finance and Stochastics, 2017, vol. 21, issue 2, No 1, 360 pages

Abstract: Abstract In this paper, which is a continuation of the discrete-time paper (Björk and Murgoci in Finance Stoch. 18:545–592, 2004), we study a class of continuous-time stochastic control problems which, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We study these problems within a game-theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled continuous-time Markov process and a fairly general objective functional, we derive an extension of the standard Hamilton–Jacobi–Bellman equation, in the form of a system of nonlinear equations, for the determination of the equilibrium strategy as well as the equilibrium value function. The main theoretical result is a verification theorem. As an application of the general theory, we study a time-inconsistent linear-quadratic regulator. We also present a study of time-inconsistency within the framework of a general equilibrium production economy of Cox–Ingersoll–Ross type (Cox et al. in Econometrica 53:363–384, 1985).

Keywords: Time-consistency; Time-inconsistency; Time-inconsistent control; Dynamic programming; Stochastic control; Bellman equation; Hyperbolic discounting; Mean-variance; Equilibrium; 49L99; 49N90; 60J70; 91A10; 91A80; 91B02; 91B25; 91B51; 91G80 (search for similar items in EconPapers)
JEL-codes: C61 C72 C73 D5 G11 G12 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (105)

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DOI: 10.1007/s00780-017-0327-5

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