โ Scribed by Glenn Shafer; Vladimir Vovk
No coin nor oath required. For personal study only.
Provides a foundation for probability based on game theory rather than measure theory.
Content: Probability and Finance as a Game --
A Game with the World --
The Protocol for a Probability Game --
The Fundamental Interpretative Hypothesis --
The Many Interpretations of Probability --
Game-Theoretic Probability in Fiannce --
Probability without Measure --
The Historical Context --
Probability before Kolmogorov --
Kolmogorov's Measure-Theoretic Framework --
Realized Randomness --
What is a Martingale? --
The Impossibility of a Gambling System --
Neosubjectivism --
The Bounded Strong Law of Large Numbers --
The Fair-Coin Game --
Forecasting a Bounded Variable --
Who Sets the Prices? --
Asymmetric Bounded Forecasting Games --
Appendix: The Computation of Strategies --
Kolmogorov's Strong Law of Large Numbers --
Two Statements of Kolmogorov's Strong Law --
Skeptic's Strategy --
Reality's Strategy --
The Unbounded Upper Forecasting Protocol --
A Martingale Strong Law --
Appendix: Martin's Theorem --
The Law of the Iterated Logarithm --
Unbounded Forecasting Protocols --
The Validity of the Iterated-Logarithm Bound --
The Sharpness of the Iterated-Logarithm Bound --
A Martingale Law of the Iterated Logarithm --
Appendix: Historical Comments --
Appendix: Kolmogorov's Finitary Interpretation --
The Weak Laws --
Bernoulli's Theorem --
De Moivre's Theorem --
A One-Sided Central Limit Theorem --
Appendix: The Gaussian Distribution --
Appendix: Stochastic Parabolic Potential Theory --
Lindeberg's Theorem --
Lindeberg Protocols --
Statement and Proof of the Theorem --
Examples of the Theorem.
๐ SIMILAR VOLUMES
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.
Provides a foundation for probability based on game theory rather than measure theory.<ul><li>A strong philosophical approach with practical applications.<li>Presents in-depth coverage of classical probability theory as well as new theory.</ul>
Probability and Finance is 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 surprising synthesis of the objective and the subjective. Practit
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.