# Glenn Shafer - Probability and Finance

#### Provides a foundation for probability based on game theory rather than measure theory.

- A strong philosophical approach with practical applications.
- Presents in-depth coverage of classical probability theory as well as new theory.

#### Review

“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)

#### From the Back Cover

A new game-theoretic approach to probability and finance

Probability and Finance presents essential reading for anyone who studies or uses probability. Mathematicians and statisticians will find in it a new framework for probability: game theory instead of measure theory. Philosophers will find a surpising synthesis of the objective and the subjective. Practitioners, especially in financial engineering, will learn new ways to understand and sometimes eliminate stochastic models.

The first half of the book explains a new mathematical and philosophical framework for probability, based on a sequential game between an idealized scientist and the world. Two very accessible introductory chapters, one presenting an overview of the new framework and one reviewing its historical context, are followed by a careful mathematical treatment of probability’s classical limit theorems.

The second half of the book, on finance, illustrates the potential of the new framework. It proposes greater use of the market and less use of stochastic models in the pricing of financial derivatives, and it shows how purely game-theoretic probability can replace stochastic models in the efficient-market hypothesis.