Pré-Publication, Document De Travail Année : 2025

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

Résumé

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.

Fichier principal
Vignette du fichier
V31_Multiple stopping problem.pdf (425.07 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-05031465 , version 1 (11-04-2025)

Licence

Identifiants

  • HAL Id : hal-05031465 , version 1

Citer

Miryana Grigorova, Marie-Claire Quenez, Peng Yuan. The non-linear multiple stopping problem: between the discrete and the continuous time. 2025. ⟨hal-05031465⟩
56 Consultations
187 Téléchargements

Partager

  • More