Time-inconsistent stopping, myopic adjustment and equilibrium stability: with a mean-variance application

Volume 122 / 2020

Sören Christensen, Kristoffer Lindensjö Banach Center Publications 122 (2020), 53-76 MSC: Primary 60G40; Secondary 91A25. DOI: 10.4064/bc122-4


For a discrete time Markov chain and in line with Strotz’ consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We consider pure and mixed stopping strategies and a (subgame perfect Nash) equilibrium. We provide different necessary and sufficient equilibrium conditions including a verification theorem. Using a fixed point argument we provide equilibrium existence results. We adapt and study the notion of the myopic adjustment process and introduce different kinds of equilibrium stability. We show that neither existence nor uniqueness of equilibria should generally be expected. The developed theory is applied to a mean-variance problem and a variance problem.


  • Sören ChristensenDepartment of Mathematics
    Kiel University
    Ludewig-Meyn-Str. 4
    D-24098 Kiel, Germany
  • Kristoffer LindensjöDepartment of Mathematics
    Stockholm University
    SE-106 91 Stockholm, Sweden

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