Day traders, traders for financial institutions, and corporate executives sometimes appear to do better than chance only because the risk of large losses is hidden or overlooked. As students of casino gambling know, one way to obscure the risk of large losses is to bet more when you are losing...

We derive formulas for the performance of capital assets in continuous time from an efficient market hypothesis, with no stochastic assumptions and no assumptions about the beliefs or preferences of investors. Our efficient market hypothesis says that a speculator with limited means cannot beat...

This paper examines the development of Laplacean practical certainty from 1810, when Laplace proved his central limit theorem, to 1925, when Ronald A. Fisher published his Statistical Methods for Research Workers.Although Laplace's explanations of the applications of his theorem were accessible...

A game-theoretic efficient market hypothesis says that a trading strategy will not multiply the capital it risks substantially relative to a specified market index. This implies that the autocorrelation of returns with respect to the index will be small and that a signal x will have...

Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- Part I Examples in Discrete Time -- Chapter 1 Borel's Law of Large Numbers -- 1.1 A Protocol for Testing Forecasts -- 1.2 A Game‐Theoretic Generalization of Borel's Theorem -- 1.3 Binary Outcomes -- 1.4 Slackenings...