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Minimax perfect stopping rules for selling an asset near its ultimate maximum

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Abstract

We study the problem of selling an asset near its ultimate maximum in the minimax setting. The regret-based notion of a perfect stopping time is introduced. A perfect stopping time is uniquely characterized by its optimality properties and has the following form: one should sell the asset if its price deviates from the running maximum by a certain time-dependent quantity. The related selling rule improves any earlier one and cannot be improved by further delay. The results, which are applicable to a quite general price model, are illustrated by several examples.

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Acknowledgments

The author is grateful to anonymous referees for stimulating suggestions, especially concerning the necessity of case studies.

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Authors and Affiliations

  1. Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, Mil’chakova str., 8a, 344090, Rostov-on-Don, Russia

    Dmitry B. Rokhlin

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  1. Dmitry B. Rokhlin
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Correspondence to Dmitry B. Rokhlin.

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The research is supported by Southern Federal University, Project 213.01-07-2014/07.

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Rokhlin, D.B. Minimax perfect stopping rules for selling an asset near its ultimate maximum. Optim Lett 11, 1743–1756 (2017). https://doi.org/10.1007/s11590-016-1091-8

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  • DOI: https://doi.org/10.1007/s11590-016-1091-8

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