ubject：On Time Consistency in Efficiency of Discrete-Time Efficient Mean-Variance Policy in a Cone Constrained Market
Speaker：Prof. Duan Li （Chinese University of Hong Kong）
Time：10:00-11:30 a.m. Aug. 30, 2012
Location：Room 712, Siyuan Building
Abstract：
The discrete-time mean-variance portfolio selection formulation does not satisfy time consistency in efficiency (TCICE) in general. Such a time inconsistency may stimulate investors’ irrational investment behavior. On the other hand, effects on the time consistency in efficiency when enforcing certain portfolio constrains have not been fully recognized or formally studied in the literature. In this research, for a convex cone constrained market, we drive the semi-analytical expressions of pre-committed efficient mean-variance policy and the variance-optimal signed supermartingale measure (VSSM). Our analysis shows that the pre-committed discrete-time efficient mean-variance policy satisfies TCIE if and only if the conditional expectation of VSSM’s density (with respect to original probability measure) is nonnegative. Once the conditional expectation takes a negative value, it remains the same until the terminal time. Our finding reveals that the property of time consistency in efficiency for a pre-committed efficient policy only depends on the basic market setting (including portfolio constraints), which motivates us to investigate how to introduce suitable portfolio constraints such that the time consistency in efficiency for dynamic portfolio selection can be guaranteed.
