Parallel Search for Information
33 Pages Posted: 16 May 2019
Date Written: May 16, 2019
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
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