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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 85, 2013 - Issue 4: Taksar Memorial Issue
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Original Articles

Mean–semivariance portfolio selection under probability distortion

, &
Pages 604-619 | Received 20 Mar 2013, Accepted 16 Apr 2013, Published online: 30 May 2013
 

Abstract

We formulate and study a mean–semivariance portfolio selection problem in continuous time when the probability is distorted by a nonlinear transformation. We give necessary and sufficient conditions for the feasibility and the existence of optimal strategies, respectively, and present the general form of optimal solutions when they exist. In sharp contrast with the previously established result that the infimum of the problem is not attainable when there is no probability distortion, we show that the infimum can be achieved with proper probability distortions. Finally, for a number of interesting cases we derive the optimal solutions in closed forms whenever they exist.

Keywords:

Notes

1. This is indeed the Choquet expectation of X with respect to the capacity (which is a nonlinear probability measure); see [Citation1].

2. This is because the first (second) equality constraint in (6) could be revised to the less-or-equal (greater-or-equal) inequality constraint without essentially changing the model.

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