(Wiley Series in Probability and Statistics) 1st Edition
by Glenn Shafer (Author), Vladimir Vovk (Author)
Game-theoretic probability and finance come of age
Glenn Shafer and Vladimir Vovk’s Probability and Finance,
published in 2001, showed that perfect-information games can be used to
define mathematical probability. Based on fifteen years of further
research, Game-Theoretic Foundations for Probability and Finance
presents a mature view of the foundational role game theory can play.
Its account of probability theory opens the way to new methods of
prediction and testing and makes many statistical methods more
transparent and widely usable. Its contributions to finance theory
include purely game-theoretic accounts of Ito’s stochastic calculus, the
capital asset pricing model, the equity premium, and portfolio theory.
Game-Theoretic Foundations for Probability and Finance
is a book of research. It is also a teaching resource. Each chapter is
supplemented with carefully designed exercises and notes relating the
new theory to its historical context.
Praise from early readers
“Ever since Kolmogorov's Grundbegriffe,
the standard mathematical treatment of probability theory has been
measure-theoretic. In this ground-breaking work, Shafer and Vovk give a
game-theoretic foundation instead. While being just as rigorous, the
game-theoretic approach allows for vast and useful generalizations of
classical measure-theoretic results, while also giving rise to new,
radical ideas for prediction, statistics and mathematical finance
without stochastic assumptions. The authors set out their theory in
great detail, resulting in what is definitely one of the most important
books on the foundations of probability to have appeared in the last few
decades.” – Peter Grünwald, CWI and University of Leiden
“Shafer
and Vovk have thoroughly re-written their 2001 book on the
game-theoretic foundations for probability and for finance. They have
included an account of the tremendous growth that has occurred since, in
the game-theoretic and pathwise approaches to stochastic analysis and
in their applications to continuous-time finance. This new book will
undoubtedly spur a better understanding of the foundations of these very
important fields, and we should all be grateful to its authors.” –
Ioannis Karatzas, Columbia University
