# The non-linear multiple stopping problem: between the discrete and the continuous time

arXiv: https://arxiv.org/abs/2504.13503 · HTML: https://mlsanity.com/paper/2504.13503/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2025.

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

- [Deep Learning for the Multiple Optimal Stopping Problem](https://mlsanity.com/paper/2512.22961/) (2025)

## Abstract (arXiv)

We consider the non-linear optimal multiple stopping problem under general conditions on the non-linear evaluation operators, which might depend on two time indices: the time of evaluation/assessment and the horizon (when the reward or loss is incurred). We do not assume convexity/concavity or cash-invariance. We focus on the case where the agent's stopping strategies are what we call Bermudan stopping strategies, a framework which can be seen as lying between the discrete and the continuous time. We first study the non-linear double optimal stopping problem by using a reduction approach. We provide a necessary and a sufficient condition for optimal pairs, and a result on existence of optimal pairs. We then generalize the results to the non-linear d-optimal stopping problem. We treat the symmetric case (of additive and multiplicative reward families) as examples.