Equilibrium concepts for time‐inconsistent stopping problems in continuous time

Erhan Bayraktar, Jingjie Zhang and Zhou Zhou

Mathematical Finance, 2021, vol. 31, issue 1, 508-530

Abstract: 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.

Date: 2021
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https://doi.org/10.1111/mafi.12293

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Working Paper: Equilibrium concepts for time-inconsistent stopping problems in continuous time (2020)
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