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Books > Science & Mathematics > Mathematics > Probability & statistics
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Game-Theoretic Foundations for Probability and Finance (Hardcover, 2 Rev Ed)
Loot Price: R2,823
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Game-Theoretic Foundations for Probability and Finance (Hardcover, 2 Rev Ed)
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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
Grunwald, 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
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