Equilibria for Time-inconsistent Singular Control Problems
Optimization and Control
2024-04-08 v2
Abstract
We study a time-inconsistent singular control problem originating from irreversible reinsurance decisions with non-exponential discount. A novel definition of equilibrium for time-inconsistent singular control problems is introduced. For the problem with non-exponential discount, both sufficient and necessary conditions are derived, providing a thorough mathematical characterization of the equilibrium. Specifically, the equilibrium can be characterized by an extended HJB system, which is a coupled system of non-local parabolic equations with free boundaries. Finally, by showing the existence of classical solutions to the extended HJB system, the existence of equilibria is established under some additional assumptions.
Cite
@article{arxiv.2310.09198,
title = {Equilibria for Time-inconsistent Singular Control Problems},
author = {Zongxia Liang and Xiaodong Luo and Fengyi Yuan},
journal= {arXiv preprint arXiv:2310.09198},
year = {2024}
}