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.
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.