Probability-free pricing of adjusted American lookbacks.

Втр, 08/23/2011 - 15:01 — SomNambul

Authors: Vladimir Vovk, Alexander Shen, A. Philip Dawid, Steven de Rooij, Glenn Shafer, Nikolai Vereshchagin, Wouter M. Koolen, Peter Grunwald
Subjects: Pricing of Securities

link: http://arxiv.org/abs/1108.4113
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 trading
in 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.

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