Parallel Search for Information

33 Pages Posted: 16 May 2019

See all articles by T. Tony Ke

T. Tony Ke

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Wenpin Tang

University of California, Los Angeles (UCLA) - Department of Mathematics

J. Miguel Villas-Boas

University of California, Berkeley

Yuming Zhang

University of California, Los Angeles (UCLA) - Department of Mathematics

Date Written: May 16, 2019

Abstract

We consider an optimal stopping problem of a d-dimensional Brownian motion, where the payoff at stopping is the maximum component of the Brownian motion, and there is a running cost before stopping. Applications include choosing one among several alternatives while learning simultaneously about all the alternatives (parallel search), and exercising an option based on several assets. We present necessary and sufficient conditions for the solution, establishing existence and uniqueness. We show that the free boundary is star-shaped, and present asymptotic characterization of the value function and the free boundary. We also show properties of how the distance between the free boundary and the diagonal varies with the number of alternatives.

Keywords: Optimal Stopping, Free Boundary Problem, Information, Search Theory, Brownian Motion

Suggested Citation

Ke, Tony and Tang, Wenpin and Villas-Boas, J. Miguel and Zhang, Yuming, Parallel Search for Information (May 16, 2019). MIT Sloan Research Paper No. 5771-19. Available at SSRN: https://ssrn.com/abstract=3389057 or http://dx.doi.org/10.2139/ssrn.3389057

Tony Ke (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Wenpin Tang

University of California, Los Angeles (UCLA) - Department of Mathematics ( email )

Los Angeles, CA 90095-1481
United States

J. Miguel Villas-Boas

University of California, Berkeley ( email )

Haas School of Business
Berkeley, CA 94720
United States
510-642-1250 (Phone)
510-643-1420 (Fax)

Yuming Zhang

University of California, Los Angeles (UCLA) - Department of Mathematics ( email )

Los Angeles, CA 90095-1481
United States

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