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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2504.13503 |
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| _version_ | 1866908325787992064 |
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| author | Grigorova, Miryana Quenez, Marie-Claire Yuan, Peng |
| author_facet | Grigorova, Miryana Quenez, Marie-Claire Yuan, Peng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The non-linear multiple stopping problem: between the discrete and the continuous time Grigorova, Miryana Quenez, Marie-Claire Yuan, Peng Optimization and Control Probability 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. |
| title | The non-linear multiple stopping problem: between the discrete and the continuous time |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2504.13503 |