Time Consistent Stopping for the Mean-Standard Deviation Problem --- The Discrete Time Case

27 Pages Posted: 5 Mar 2018  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Jingjie Zhang

University of Michigan at Ann Arbor - Department of Mathematics

Zhou Zhou

University of Minnesota - Twin Cities

Date Written: February 23, 2018

Abstract

Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to consider the notion of liquidation strategies, which lets the stopping right to be divisible. We then argue that the mean-standard deviation variant of this problem makes more sense for this type of strategies in terms of time consistency. It turns out that an equilibrium liquidation strategy always exists. We then analyze whether optimal equilibrium liquidation strategies exist and whether they are unique and observe that neither may hold.

Keywords: Time-inconsistency, optimal stopping, liquidation strategy, mean-variance problem, subgame perfect Nash equilibrium

Suggested Citation

Bayraktar, Erhan and Zhang, Jingjie and Zhou, Zhou, Time Consistent Stopping for the Mean-Standard Deviation Problem --- The Discrete Time Case (February 23, 2018). Available at SSRN: https://ssrn.com/abstract=3128866 or http://dx.doi.org/10.2139/ssrn.3128866

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Jingjie Zhang

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Zhou Zhou

University of Minnesota - Twin Cities ( email )

420 Delaware St. SE
Minneapolis, MN 55455
United States

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