Insuring against loss of evidence in game-theoretic probability
Abstract
We consider the game-theoretic scenario of testing the performance of Forecaster by Sceptic who gambles against the forecasts. Sceptic's current capital is interpreted as the amount of evidence he has found against Forecaster. Reporting the maximum of Sceptic's capital so far exaggerates the evidence. We characterize the set of all increasing functions that remove the exaggeration. This result can be used for insuring against loss of evidence.
Keywords
Cite
@article{arxiv.1005.1811,
title = {Insuring against loss of evidence in game-theoretic probability},
author = {A. Philip Dawid and Steven de Rooij and Glenn Shafer and Alexander Shen and Nikolai Vereshchagin and Vladimir Vovk},
journal= {arXiv preprint arXiv:1005.1811},
year = {2010}
}
Comments
7 pages. This version (version 2) is identical to version 1 (May 2010). The most up-to-date version can be found at http://www.probabilityandfinance.com/ (Working Paper 34). That version includes an application to financial markets (in which case our result can be used for insuring against loss of the accumulated capital); The Game-Theoretic Probability and Finance Project, Working Paper 34