NDLI: On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Lindensjö, Kristoffer Christensen, Sören
Copyright Year	2018
Abstract	Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a straightforward way be applied to nonstandard stopping problems without this time-consistent structure. This paper is devoted to the solution of time-inconsistent stopping problems with the reward depending on the initial state using an adaptation of Strotz's consistent planning. More precisely, we give a precise equilibrium definition---of the type subgame perfect Nash equilibrium based on pure Markov strategies. In general, such equilibria do not always exist and if they exist they are in general not unique. We, however, develop an iterative approach to finding equilibrium stopping times for a general class of problems and apply this approach to one-sided stopping problems on the real line. We furthermore prove a verification theorem based on a set of variational inequalities which also allows us to find equilibria. In the case of a standard optimal stopping problem, we investigate the connection between the notion of an optimal and an equilibrium stopping time. As an application of the developed theory we study a selling strategy problem under exponential utility and endogenous habit formation.
Starting Page	4228
Ending Page	4255
Page Count	28
File Format	PDF
ISSN	03630129
DOI	10.1137/17M1153029
e-ISSN	10957138
Issue Number	6
Volume Number	56
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-11-27
Access Restriction	Subscribed
Subject Keyword	Markov process optimal stopping Noncooperative games time-inconsistency Applications of Brownian motions and diffusion theory Fundamental topics subgame perfect Nash equilibrium variational inequalities Dynamic stochastic general equilibrium theory Financial applications of other theories Dynamic games Stopping times; optimal stopping problems; gambling theory Strotz's consistent planning
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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