Projects per year
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 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.
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.
Original language  Undefined/Unknown 

Number of pages  28 
Publication status  Published  20 Aug 2011 
Keywords
 qfin.PR
 91G20, 60G42
Projects
 1 Finished

The Decision Theory of Hiring and Firing Advisors
Vovk, V. (PI)
Netherlands Organisation for Scientific Research
1/02/11 → 31/01/13
Project: Research