The value of foresight
File(s)
Published version
Author(s)
Ernst, Philip A
Rogers, LCG
Zhou, Quan
Type
Journal Article
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
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
Date Issued
2017-12
Date Acceptance
2017-03-22
Citation
Stochastic Processes and their Applications, 2017, 127 (12), pp.3913-3927
ISSN
0304-4149
Publisher
Elsevier BV
Start Page
3913
End Page
3927
Journal / Book Title
Stochastic Processes and their Applications
Volume
127
Issue
12
Copyright Statement
c⃝ 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Identifier
https://www.sciencedirect.com/science/article/pii/S0304414917300923?via%3Dihub
Subjects
Statistics & Probability
0102 Applied Mathematics
0104 Statistics
1502 Banking, Finance and Investment
Publication Status
Published