Stopping Behaviors of Naive and Non-Committed Sophisticated Agents When They Distort Probability

36 Pages Posted: 13 Sep 2017

See all articles by Yu-Jui Huang

Yu-Jui Huang

University of Colorado at Boulder - Department of Applied Mathematics

Adrien Nguyen-Huu

Université Montpellier I

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: September 11, 2017

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 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. In particular, we show how such strategic reasoning may turn a naive 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, naive and sophisticated agents, equilibrium stopping law

JEL Classification: G11, I12

Suggested Citation

Huang, Yu-Jui and Nguyen-Huu, Adrien and Zhou, Xunyu, Stopping Behaviors of Naive and Non-Committed Sophisticated Agents When They Distort Probability (September 11, 2017). Available at SSRN: https://ssrn.com/abstract=3035538 or http://dx.doi.org/10.2139/ssrn.3035538

Yu-Jui Huang (Contact Author)

University of Colorado at Boulder - Department of Applied Mathematics ( email )

Boulder, CO 80309
United States

HOME PAGE: http://www.yujui-huang.com

Adrien Nguyen-Huu

Université Montpellier I ( email )

Avenue de la Mer Site Richter
163 Rue Auguste Broussonnet
Montpellier, Cedex 2 34090
France

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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