 General stopping behaviors of naive and non-committed sophisticated agents, with application to probability distortionYu-Jui Huang (yujui.huang@dcu.ie),
Adrien Nguyen-Huu and
Xun Yu Zhou (yu.zhou2012@gmail.com)
Post-Print from HAL Abstract: We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naive agents who reoptimize continuously in time, as well as equilibrium strategies of sophisticated agents who anticipate but lack control over their future selves' behaviors. When the state process is one dimensional and the payoff functional satisfies some regularity conditions, we prove that any equilibrium can be obtained as a fixed point of an operator. This operator represents strategic reasoning that takes the future selves' behaviors into account. We then apply the general results to the case when the agents distort probability and the diffusion process is a geometric Brownian motion. The problem is inherently time-inconsistent as the level of distortion of a same event changes over time. We show how the strategic reasoning may turn a naive agent into a sophisticated one. Moreover, we derive stopping strategies of the two types of agent for various parameter specifications of the problem, illustrating rich behaviors beyond the extreme ones such as "never-stopping" or "never-starting". Date: 2019 Published in Mathematical Finance, inPress, ⟨10.1111/mafi.12224⟩ There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-02110872 DOI: 10.1111/mafi.12224 Access Statistics for this paper More papers in Post-Print from HAL |
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