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Title: Mean-variance policy for discrete-time cone-constrained markets: Time consistency in efficiency and the minimum-variance signed supermartingale measure
Authors: Cui, X
Li, D
Li, X 
Keywords: Cone-constrained market
Discrete-time mean-variance policy
Minimum-variance signed supermartingale measure
Time consistency in efficiency
Issue Date: 2015
Publisher: Blackwell Publishing Inc.
Source: Mathematical finance, 2015 How to cite?
Journal: Mathematical Finance 
Abstract: The discrete-time mean-variance portfolio selection formulation, which is a representative of general dynamic mean-risk portfolio selection problems, typically does not satisfy time consistency in efficiency (TCIE), i.e., a truncated precommitted efficient policy may become inefficient for the corresponding truncated problem. In this paper, we analytically investigate the effect of portfolio constraints on the TCIE of convex cone-constrained markets. More specifically, we derive semi-analytical expressions for the precommitted efficient mean-variance policy and the minimum-variance signed supermartingale measure (VSSM) and examine their relationship. Our analysis shows that the precommitted discrete-time efficient mean-variance policy satisfies TCIE if and only if the conditional expectation of the density of the VSSM (with respect to the original probability measure) is nonnegative, or once the conditional expectation becomes negative, it remains at the same negative value until the terminal time. Our finding indicates that the TCIE property depends only on the basic market setting, including portfolio constraints.
ISSN: 0960-1627
DOI: 10.1111/mafi.12093
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