# Approximation of Singular-Stopping Control Driven by Hawkes Processes via Rescaled MDPs

arXiv: https://arxiv.org/abs/2602.05025 · HTML: https://mlsanity.com/paper/2602.05025/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2026.

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

- [Continuous-Time Reinforcement Learning for Controlled Hawkes Jump-Diffusions](https://mlsanity.com/paper/2608.19151/) (2026)

## Abstract (arXiv)

We investigate a singular-optimal stopping stochastic control problem driven by self-exciting dynamics governed by a Hawkes process. In the continuous-time setting, we show that the optimization problem reduces to solving a variational partial differential equation with gradient constraints. We then introduce its discrete-time counterpart, modeled as a Markov Decision Process. We prove that, under an appropriate rescaling procedure, the value function of the discrete-time problem converges to its continuous-time equivalent, implying that the discrete-time optimizers are asymptotically optimal for the continuous-time problem. Finally, we apply these results to an Ornstein-Uhlenbeck stochastic differential equation driven by a Hawkes process with singular control, motivated by optimal power plant investment under cyber threat and we illustrate the theoretical findings through numerical simulations.