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The value of foresight

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  • Philip Ernst
  • L. C. G. Rogers
  • Quan Zhou

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.

Suggested Citation

  • Philip Ernst & L. C. G. Rogers & Quan Zhou, 2016. "The value of foresight," Papers 1601.05872, arXiv.org, revised Jul 2016.
    • Handle: RePEc:arx:papers:1601.05872
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    References listed on IDEAS

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    1. Acciaio, Beatrice & Fontana, Claudio & Kardaras, Constantinos, 2016. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1761-1784.
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    Cited by:

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    2. Philip A. Ernst & James R. Thompson & Yinsen Miao, 2017. "Tukey’s transformational ladder for portfolio management," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(3), pages 317-355, August.
    3. Lee, Susan E. & Braithwaite, Peter & Leach, Joanne M. & Rogers, Chris D.F., 2016. "A comparison of energy systems in Birmingham, UK, with Masdar City, an embryonic city in Abu Dhabi Emirate," Renewable and Sustainable Energy Reviews, Elsevier, vol. 65(C), pages 1299-1309.
    4. Fabrice Baudoin & Oleksii Mostovyi, 2024. "The indifference value of the weak information," Papers 2408.02137, arXiv.org.
    5. José Manuel Corcuera & Giulia Di Nunno, 2018. "Kyle–Back’S Model With A Random Horizon," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-41, March.
    6. Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.

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