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Optimal stopping: Bermudan strategies meet non-linear evaluations
- Publication Year :
- 2023
-
Abstract
- We address an optimal stopping problem over the set of Bermudan-type strategies $\Theta$ (which we understand in a more general sense than the stopping strategies for Bermudan options in finance) and with non-linear operators (non-linear evaluations) assessing the rewards, under general assumptions on the non-linear operators $\rho$. We provide a characterization of the value family V in terms of what we call the ($\rho$,$\Theta$) -Snell envelope of the pay-off family. We establish a Dynamic Programming Principle. We provide an optimality criterion in terms of a ($\rho$,$\Theta$) -martingale property of V on a stochastic interval. We investigate the ($\rho$,$\Theta$)-martingale structure and we show that the ''first time'' when the value family coincides with the pay-off family is optimal. The reasoning simplifies in the case where there is a finite number n of pre-described stopping times, where n does not depend on the scenario $\omega$. We provide examples of non-linear operators entering our framework.
- Subjects :
- Mathematics - Optimization and Control
Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2301.11102
- Document Type :
- Working Paper