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Equilibrium concepts for time‐inconsistent stopping problems in continuous time
Author(s) -
Bayraktar Erhan,
Zhang Jingjie,
Zhou Zhou
Publication year - 2021
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12293
Subject(s) - optimal stopping , stopping time , subgame perfect equilibrium , markov perfect equilibrium , mathematical economics , nash equilibrium , subadditivity , markov chain , optional stopping theorem , dynamic inconsistency , mathematics , economics , mathematical optimization , combinatorics , statistics
A new notion of equilibrium, which we call strong equilibrium , is introduced for time‐inconsistent stopping problems in continuous time. Compared to the existing notions introduced in Huang, Y.‐J., & Nguyen‐Huu, A. (2018, Jan 01). Time‐consistent stopping under decreasing impatience. Finance and Stochastics , 22(1), 69–95 and Christensen, S., & Lindensjö, K. (2018). On finding equilibrium stopping times for time‐inconsistent markovian problems. SIAM Journal on Control and Optimization , 56(6), 4228–4255, which in this paper are called mild equilibrium and weak equilibrium , respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous‐time Markov chain and the discount function is log subadditive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence.