General Stopping Behaviors of Naïve and Noncommitted Sophisticated Agents, with Application to Probability Distortion

31 Pages Posted: 29 May 2020

See all articles by Yu-Jui Huang

Yu-Jui Huang

University of Colorado at Boulder - Department of Applied Mathematics

Adrien Nguyen‐Huu

affiliation not provided to SSRN

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Date Written: January 2020

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 naïve 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 naïve 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.”

Keywords: equilibrium stopping law, naïve and sophisticated agents, optimal stopping, probability distortion, time inconsistency

Suggested Citation

Huang, Yu-Jui and Nguyen‐Huu, Adrien and Zhou, Xun Yu, General Stopping Behaviors of Naïve and Noncommitted Sophisticated Agents, with Application to Probability Distortion (January 2020). Mathematical Finance, Vol. 30, Issue 1, pp. 310-340, 2020, Available at SSRN: https://ssrn.com/abstract=3613906 or http://dx.doi.org/10.1111/mafi.12224

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

affiliation not provided to SSRN

No Address Available

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong
852 2609-8320 (Phone)
852 2603-5505 (Fax)

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