Stopping Behaviors of Naïve and Non-Committed Sophisticated Agents when They Distort Probability

Comportement d'arrêt des agents naïfs et sophistiqués sous distorsion des probabilités perçues

Yu-Jui Huang (), Adrien Nguyen-Huu and Xun Yu Zhou ()
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Yu-Jui Huang: University of Colorado - Department of Applied Mathematics - University of Colorado [Boulder]
Xun Yu Zhou: Columbia University [New York]

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Abstract: We consider the problem of stopping a diffusion process with a payoff functional involving probability distortion. The problem is inherently time-inconsistent as the level of distortion of a same event changes over time. We study stopping decisions of na¨ıvena¨ıve 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. In particular, we show how such strategic reasoning may turn a na¨ıvena¨ıve agent into a sophisticated one. Finally, when the diffusion process is a geometric Brownian motion we derive stopping strategies of these 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 ".

Keywords: Optimal stopping; probability distortion; time inconsistency; naïve and sophisticated agents; equilibrium stopping law (search for similar items in EconPapers)
Date: 2017-09-11
Note: View the original document on HAL open archive server: https://hal.science/hal-01586655v1
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