Equilibria for Time-inconsistent Singular Control Problems

Fuente: arXiv
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Main Authors: Liang, Zongxia, Luo, Xiaodong, Yuan, Fengyi
Format: Preprint
Published: 2023
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author Liang, Zongxia
Luo, Xiaodong
Yuan, Fengyi
author_facet Liang, Zongxia
Luo, Xiaodong
Yuan, Fengyi
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2310_09198
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Equilibria for Time-inconsistent Singular Control Problems
Liang, Zongxia
Luo, Xiaodong
Yuan, Fengyi
Optimization and Control
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.
title Equilibria for Time-inconsistent Singular Control Problems
topic Optimization and Control
url https://arxiv.org/abs/2310.09198