On time-inconsistent stochastic control in continuous time

By Tomas Björk, Mariana Khapko, Agatha Murgoci. Finance and Stochastics, 2017

333 citations recorded by the source corpus.

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).

Subfields: Economics and Econometrics, Finance, General Decision Sciences

View Paper: https://www.semanticscholar.org/paper/852b015a3e21a71b3e161b0e6dcb630a48ecb37e

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Citations in the corpus

McKean–Vlasov optimal control: The dynamic programming principle (2019, background): “One of the main reasons is actually a very bleak one for us: due to the non–linear dependency with respect to the law of process, the problem is actually a time inconsistent control problem (like the classical mean–variance optimisation problem in finance, see the recent papers by Björk and Murgoci ”
Bellman equation and viscosity solutions for mean-field stochastic control problem (2015, neutral): “It is claimed in [8,38] that Bellman optimality principle does not hold, and therefore the problem is time-inconsistent.”
On time-inconsistent stopping problems and mixed strategy stopping times (2018, methodology): “In [5] a meanvariance control problem is studied using the general game-theoretic framework for timeinconsistent stochastic control of [3].”