**Probability-free pricing of adjusted American lookbacks.** / Philip Dawid, A.; de Rooij, Steven; Grunwald, Peter; M. Koolen, Wouter; Shafer, Glenn; Shen, Alexander; Vereshchagin, Nikolai; Vovk, Vladimir.

Research output: Working paper

Published

**Probability-free pricing of adjusted American lookbacks.** / Philip Dawid, A.; de Rooij, Steven; Grunwald, Peter; M. Koolen, Wouter; Shafer, Glenn; Shen, Alexander; Vereshchagin, Nikolai; Vovk, Vladimir.

Research output: Working paper

Philip Dawid, A, de Rooij, S, Grunwald, P, M. Koolen, W, Shafer, G, Shen, A, Vereshchagin, N & Vovk, V 2011 'Probability-free pricing of adjusted American lookbacks'.

Philip Dawid, A., de Rooij, S., Grunwald, P., M. Koolen, W., Shafer, G., Shen, A., Vereshchagin, N., & Vovk, V. (2011). *Probability-free pricing of adjusted American lookbacks*.

Philip Dawid A, de Rooij S, Grunwald P, M. Koolen W, Shafer G, Shen A et al. Probability-free pricing of adjusted American lookbacks. 2011 Aug 20.

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title = "Probability-free pricing of adjusted American lookbacks",

abstract = "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 capitalX_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.",

keywords = "q-fin.PR, 91G20, 60G42",

author = "{Philip Dawid}, A. and {de Rooij}, Steven and Peter Grunwald and {M. Koolen}, Wouter and Glenn Shafer and Alexander Shen and Nikolai Vereshchagin and Vladimir Vovk",

note = "arXiv technical report 28 pages, 1 figure",

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T1 - Probability-free pricing of adjusted American lookbacks

AU - Philip Dawid, A.

AU - de Rooij, Steven

AU - Grunwald, Peter

AU - M. Koolen, Wouter

AU - Shafer, Glenn

AU - Shen, Alexander

AU - Vereshchagin, Nikolai

AU - Vovk, Vladimir

N1 - arXiv technical report 28 pages, 1 figure

PY - 2011/8/20

Y1 - 2011/8/20

N2 - 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 capitalX_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.

AB - 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 capitalX_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.

KW - q-fin.PR

KW - 91G20, 60G42

M3 - Working paper

BT - Probability-free pricing of adjusted American lookbacks

ER -