"Shafer...and Vovk...explain how probability can be based on game theory rather than measure theory, and how doing so allows it to be used in finance with out a lot of distracting an confusing assumptions about randomness." (Reference & Research Book News, November 2001)
"....an interesting new mathematical and philosophical framework for probability..." (Zentralblatt Math, Vol.985, No.10, 2002)
"...a creative, entertaining and imaginative book..." (Short Book Reviews, August 2002)
"The first half of this truly original book introduces a novel approach to probability, founded on game theory rather than measure theory. In an admirably clear, scholarly and engaging manner, it traces its historical antecedents, expounds its advantages, develops its technicalities, and addresses its philosophical implications. The second half goes on to do the same for financial modelling. This is a book that should utterly change the way we think about its two topics."
Philip Dawid (University College London, UK)
Probability and Finance as a Game.
PROBABILITY WITHOUT MEASURE.
The Historical Context.
The Bounded Strong Law of Large Numbers.
Kolmogorov's Strong Law of Large Numbers.
The Law of the Iterated Logarithm.
The Weak Laws.
The Generality of Probability Games.
FINANCE WITHOUT PROBABILITY.
Game-Theoretic Probability in Finance.
Games for Pricing Options in Discrete Time.
Games for Pricing Options in Continuous Time.
The Generality of Game-Theoretic Pricing.
Games for American Options.
Games for Diffusion Processes.
The Game-Theoretic Efficient-Market Hypothesis.