Philip Dawid, A., de Rooij, Steven, Grunwald, Peter, M. Koolen, Wouter, Shafer, Glenn, Shen, Alexander, Vereshchagin, Nikolai and Vovk, Vladimir (2011) Probability-free pricing of adjusted American lookbacks.
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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 X_0\int_{X_0}^{\infty}G(x)x^{-2}dx (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.
This is a Submitted version This version's date is: 20/8/2011 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/86ccdbcc-4736-2d6c-b8d7-acc5296bce59/7/
Deposited by Research Information System (atira) on 22-Jul-2014 in Royal Holloway Research Online.Last modified on 22-Jul-2014
arXiv technical report 28 pages, 1 figure