# Equilibria for Time-inconsistent Singular Control Problems

arXiv: https://arxiv.org/abs/2310.09198 · HTML: https://mlsanity.com/paper/2310.09198/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2023.

## Built on by (most cited first, 2 of 2)

- [A Reinforcement Learning Framework for Some Singular Stochastic Control Problems](https://mlsanity.com/paper/2506.22203/) (2025)
- [Reinforcement learning for irreversible reinsurance problems: the randomized singular control approach](https://mlsanity.com/paper/2512.02769/) (2025)

## Abstract (arXiv)

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.