# Reinforcement learning for irreversible reinsurance problems: the randomized singular control approach

arXiv: https://arxiv.org/abs/2512.02769 · HTML: https://mlsanity.com/paper/2512.02769/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 14 of 14)

- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [q-Learning in Continuous Time](https://mlsanity.com/paper/2207.00713/) (2022)
- [Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approach](https://mlsanity.com/paper/2108.06655/) (2021)
- [Continuous-time q-learning for mean-field control problems](https://mlsanity.com/paper/2306.16208/) (2023)
- [Randomized Optimal Stopping Problem in Continuous time and Reinforcement Learning Algorithm](https://mlsanity.com/paper/2208.02409/) (2022)
- [Unified continuous-time q-learning for mean-field game and mean-field control problems](https://mlsanity.com/paper/2407.04521/) (2024)
- [On optimal tracking portfolio in incomplete markets: The reinforcement learning approach](https://mlsanity.com/paper/2311.14318/) (2023)
- [Continuous-time Risk-sensitive Reinforcement Learning via Quadratic Variation Penalty](https://mlsanity.com/paper/2404.12598/) (2024)
- [Learning to Optimally Stop Diffusion Processes, with Financial Applications](https://mlsanity.com/paper/2408.09242/) (2024)
- [Exploratory Optimal Stopping: A Singular Control Formulation](https://mlsanity.com/paper/2408.09335/) (2024)
- [Equilibria for Time-inconsistent Singular Control Problems](https://mlsanity.com/paper/2310.09198/) (2023)
- [A Reinforcement Learning Framework for Some Singular Stochastic Control Problems](https://mlsanity.com/paper/2506.22203/) (2025)
- [Entropy Regularization in Mean-Field Games of Optimal Stopping](https://mlsanity.com/paper/2509.18821/) (2025)
- [Equilibrium Strategies for Singular Dividend Control Problems under the Mean-Variance Criterion](https://mlsanity.com/paper/2511.08433/) (2025)

## Built on by (most cited first, 1 of 1)

- [Continuous-time reinforcement learning for optimal switching over multiple regimes](https://mlsanity.com/paper/2512.04697/) (2025)

## Abstract (arXiv)

This paper studies the continuous-time reinforcement learning for stochastic singular control with the application to an infinite-horizon irreversible reinsurance problem. The singular control is equivalently characterized as a pair of regions of time and the augmented states, called the singular control law. To encourage the exploration in the learning procedure, we propose a randomization method by considering an auxiliary singular control and entropy regularization. The exploratory singular control problem is formulated as a two-stage optimal control problem, in which the time-inconsistency issue arises in the outer problem. Existence of equilibrium singular control law for the time-inconsistent outer problem is rigorously established. Taking advantage of the solution structure, we utilize a proper parameterization and neural networks to devise the actor-critic reinforcement learning algorithm. In the numerical experiment, we show the superior convergence of parameter iterations based on the randomized equilibrium policy and illustrate how the exploration may advance the learning performance.