The value of foresight

Philip A. Ernst, L.C.G. Rogers and Quan Zhou

Stochastic Processes and their Applications, 2017, vol. 127, issue 12, 3913-3927

Abstract: Suppose you have one unit of stock, currently worth 1, which you must sell before time T. The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, the expected discounted value we get when we sell will be 1. Suppose however that we are able to see a units of time into the future, and base our stopping rule on that; we should be able to do better than expected value 1. But how much better can we do? And how would we exploit the additional information? The optimal solution to this problem will never be found, but in this paper we establish remarkably close bounds on the value of the problem, and we derive a fairly simple exercise rule that manages to extract most of the value of foresight.

Keywords: Explicit stopping rules; Excursion processes; Insider trading; Bermudan fixed-window lookback option; Brownian motion (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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Working Paper: The value of foresight (2016)
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DOI: 10.1016/j.spa.2017.03.019

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