Optimal Stopping Under Probability Distortions

Denis Belomestny () and Volker Krätschmer ()
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Denis Belomestny: Duisburg-Essen University, D-45127 Essen, Germany; and IITP RAS, Moscow, Russia
Volker Krätschmer: Duisburg-Essen University, D-45127 Essen, Germany

Mathematics of Operations Research, 2017, vol. 42, issue 3, 806-833

Abstract: In this paper we study optimal stopping problems with respect to distorted expectations with concave distortion functions. Our starting point is a seminal work of Xu and Zhou in 2013, who gave an explicit solution of such a stopping problem under a rather large class of distortion functionals. In this paper, we continue this line of research and prove a novel representation, which relates the solution of an optimal stopping problem under distorted expectation to the sequence of standard optimal stopping problems and hence makes the application of the standard dynamic programming-based approaches possible. Furthermore, by means of the well-known Kusuoka representation, we extend our results to optimal stopping under general law invariant coherent risk measures. Finally, based on our representations, we develop several Monte Carlo approximation algorithms and illustrate their power for optimal stopping under absolute semideviation risk measures.

Keywords: coherent risk measures; average value-at-risk; optimal stopping; time-consistency (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:42:y:2017:i:3:p:806-833

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