A Deterministic Linear Quadratic Time-Inconsistent Optimal Control Problem
By Jiongmin Yong. 2011
81 citations recorded by the source corpus.
A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with a quadratic cost functional. A notion of time-consistent equilibrium strategy is introduced for the original time-inconsistent problem. Under certain conditions, we construct an equilibrium strategy which can be represented via a Riccati--Volterra integral equation system. Our approach is based on a study of multi-person hierarchical differential games.
Subfields: Computational Theory and Mathematics, Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/5376dc3008e0b9156679fbf0e857b801989d9d63
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Citations in the corpus
- Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations --- Time-Consistent Solutions (2013, background): “This result is comparable with those in [25], where a closed-loop equilibrium solution was obtained for deterministic LQ problems with general discounting (without conditional expectation terms).”
- Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation (2012, methodology): “As a major contribution of this paper, we have derived the equilibrium Hamilton-Jacobi-Bellman equation which can be used to characterize the equilibrium value function V (· , ·), and it recovers the result for time-inconsistent deterministic linearquadratic problem presented in [27].”