Probability-free pricing of adjusted American lookbacks

A. Philip Dawid, Steven de Rooij, Peter Grunwald, Wouter M. Koolen, Glenn Shafer, Alexander Shen, Nikolai Vereshchagin, Vladimir Vovk

Research output: Working paper

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Consider an American option that pays G(X^*_t) when exercised at time t, where G is a positive increasing function, X^*_t := \sup_{s\le t}X_s, and X_s is the price of the underlying security at time s. Assuming zero interest rates, we show that the seller of this option can hedge his position by tradingin the underlying security if he begins with initial capital
(and this is the smallest initial capital that allows him to hedge his position). This leads to strategies for trading that are always competitive both with a given strategy's current performance and, to a somewhat lesser degree, with its best performance so far. It also leads to methods of statistical testing that avoid sacrificing too much of the maximum statistical significance that they achieve in the course of accumulating data.
Original languageUndefined/Unknown
Number of pages28
Publication statusPublished - 20 Aug 2011


  • q-fin.PR
  • 91G20, 60G42

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