Optimal stopping with dynamic variational preferences
type: Item
instance of: scholarly article
title: Optimal stopping with dynamic variational preferences
zbMATH Open document ID: 1276.60049
author: Daniel Engelage
published in: Journal of Economic Theory
publication date: 2011-10-28T00:00:00Z
full work available at URL: http://hdl.handle.net/10419/37035
review text: In the classical optimal stopping problems (see [\textit{Y. S.~Chow, H.~Robbins} and \textit{D.~Siegmund}, Great expectations: the theory of optimal stopping. Boston etc.: Houghton Mifflin Company (1971; Zbl 0233.60044); \textit{G.~Peskir} and \textit{A.~Shiryaev}, Optimal stopping and free-boundary problems. Basel: Birkhäuser (2006; Zbl 1115.60001)]), the decision maker is searching for the stopping time \(\tau\) in some class which minimizes (or maximizes) the expected gain \(\operatorname{E}g(X_\tau)\), where \(g\) is a given utility function and \(\{X_t\}_{t\geq 0}\) is a well-defined stochastic process. This paper is devoted to the generalization of the optimal stopping problem when the underlined process is not fixed. Based on \textit{F. Riedel}'s [Econometrica 77, No. 3, 857--908 (2009; Zbl 1181.60064)] results the concept of variational supermartingales and variational Snell envelopes with an accompanying theory is introduced. The theory is illustrated by examples.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 5965269
zbMATH Keywords: optimal stopping
zbMATH Keywords: uncertainty aversion
zbMATH Keywords: dynamic variational preferences
zbMATH Keywords: dynamic convex risk measures
zbMATH Keywords: dynamic penalty
zbMATH Keywords: time consistency
zbMATH Keywords: multiplier preferences
zbMATH Keywords: entropic risk
zbMATH Keywords: average value at risk
reviewed by: Krzysztof J. Szajowski
describes a project that uses: QRM
MaRDI profile type: Publication
OpenAlex ID: W2072015828
cites work: Coherent measures of risk
cites work: Coherent multiperiod risk adjusted values and Bellman's principle
cites work: Dynamic risk measures: Time consistency and risk measures from BMO martingales
cites work: Dynamic monetary risk measures for bounded discrete-time processes
cites work: RISK MEASURES ON ORLICZ HEARTS
cites work: I-divergence geometry of probability distributions and minimization problems
cites work: Mutual absolute continuity of multiple priors
cites work: Recursive multiple-priors.
cites work: Convex measures of risk and trading constraints
cites work: Stochastic finance. An introduction in discrete time
cites work: Convex risk measures and the dynamics of their penalty functions
cites work: Robust Preferences and Robust Portfolio Choice
cites work: A Representation Theorem for "Preference for Flexibility"
cites work: Ambiguity Aversion, Robustness, and the Variational Representation of Preferences
cites work: Dynamic variational preferences
cites work: Q5706744
cites work: Q4114574
cites work: Q4357507
cites work: Dynamic coherent risk measures
cites work: Optimal Stopping With Multiple Priors
cites work: Q5638112
cites work: Risk measures via \(g\)-expectations
cites work: Optimal investments for risk- and ambiguity-averse preferences: a duality approach
DOI: 10.1016/J.JET.2011.06.014
description: scientific article; zbMATH DE number 5965269