On the Time-Inconsistent Deterministic Linear-Quadratic Control
Mathematical Finance
2021-10-13 v3
Abstract
A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general time-inconsistent deterministic LQ problem, where the inconsistency arises from non-exponential discount functions. By studying the solvability of the Riccati equation, we show the existence and uniqueness of the linear equilibrium for the time-inconsistent LQ problem.
Cite
@article{arxiv.2105.03670,
title = {On the Time-Inconsistent Deterministic Linear-Quadratic Control},
author = {Hongyan Cai and Danhong Chen and Yunfei Peng and Wei Wei},
journal= {arXiv preprint arXiv:2105.03670},
year = {2021}
}