Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5947
Title: Optimal stopping under probability distortion
Authors: Xu, Z 
Zhou, XY
Issue Date: Feb-2013
Source: Annals of applied probability, Feb. 2013, v. 23, no. 1, p. 251-282
Abstract: We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can then be recovered from the obtained distribution/quantile function, either in a straightforward way for several important cases or in general via the Skorokhod embedding. This approach enables us to solve the problem in a fairly general manner with different shapes of the payoff and probability distortion functions. We also discuss economical interpretations of the results. In particular, we justify several liquidation strategies widely adopted in stock trading, including those of “buy and hold,” “cut loss or take profit,” “cut loss and let profit run” and “sell on a percentage of historical high.”
Keywords: Optimal stopping
Probability distortion
Choquet expectation
Probability distribution/qunatile function
Skorokhod embedding
S-shaped and reverse S-shaped function
Publisher: Institute of Mathematical Statistics
Journal: Annals of applied probability 
ISSN: 1050-5164 (print)
2168-8737 (online)
DOI: 10.1214/11-AAP838
Rights: © Institute of Mathematical Statistics, 2013
The following article is available at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoap
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