MEAN-VARIANCE POLICY FOR DISCRETE-TIME CONE-CONSTRAINED MARKETS: TIME CONSISTENCY IN EFFICIENCY AND THE MINIMUM-VARIANCE SIGNED SUPERMARTINGALE MEASURE

Xiangyu Cui, Duan Li, Xun Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

32 Citations (Scopus)

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. This motivates us to establish a general procedure for constructing TCIE dynamic portfolio selection problems by introducing suitable portfolio constraints.
Original languageEnglish
Pages (from-to)471-504
Number of pages34
JournalMathematical Finance
Volume27
Issue number2
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • cone-constrained market
  • discrete-time mean-variance policy
  • minimum-variance signed supermartingale measure
  • time consistency in efficiency

ASJC Scopus subject areas

  • Accounting
  • Social Sciences (miscellaneous)
  • Finance
  • Economics and Econometrics
  • Applied Mathematics

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