Game-Theoretic Foundations for Probability and Finance

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 Gr nwald, 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

《博弈理論概率與金融的成熟》

格倫·謝弗（Glenn Shafer）和弗拉迪米爾·沃夫克（Vladimir Vovk）於2001年出版的《概率與金融》一書，展示了完全信息博弈可用於定義數學概率。基於十五年的進一步研究，《博弈理論基礎與概率金融》呈現了博弈理論在基礎角色中的成熟觀點。其對概率理論的描述開啟了新的預測和測試方法，使許多統計方法更加透明且廣泛可用。其對金融理論的貢獻包括對伊藤隨機微積分、資本資產定價模型、股票溢價和投資組合理論的純博弈理論描述。

《博弈理論基礎與概率金融》是一本研究書籍，也是一個教學資源。每一章都配有精心設計的練習和註解，將新理論與其歷史背景相關聯。

早期讀者的讚譽：

「自從科爾莫哥洛夫的《概率論基礎》以來，概率論的標準數學處理一直是測度論。在這部開創性的作品中，謝弗和沃夫克提供了一個博弈理論的基礎。儘管同樣嚴謹，博弈理論的方法允許對傳統測度論結果進行廣泛且有用的概括，同時也產生了在沒有隨機假設的情況下進行預測、統計和數學金融的新的激進思想。作者詳細介紹了他們的理論，結果無疑是近幾十年來關於概率基礎的最重要的書籍之一。」- 彼得·格倫瓦爾德（Peter Grünwald），CWI和萊頓大學

「謝弗和沃夫克徹底重寫了他們2001年關於博弈理論基礎的概率和金融的書籍。他們包括了自那時以來在博弈理論和路徑分析以及其在連續時間金融中的應用方面取得的巨大增長。這本新書無疑將促進對這些非常重要領域基礎的更好理解，我們都應該對作者表示感謝。」- 伊奧安尼斯·卡拉查斯（Ioannis Karatzas），哥倫比亞大學

Glenn Shafer is University Professor at Rutgers University.

Vladimir Vovk is Professor in the Department of Computer Science at Royal Holloway, University of London.

Shafer and Vovk are the authors of Probability and Finance: It's Only a Game, published by Wiley and co-authors of Algorithmic Learning in a Random World. Shafer's other previous books include A Mathematical Theory of Evidence and The Art of Causal Conjecture.

Glenn Shafer是Rutgers University的大學教授。Vladimir Vovk是倫敦大學皇家霍洛威計算機科學系的教授。Shafer和Vovk是Wiley出版的《Probability and Finance: It's Only a Game》的作者，也是《Algorithmic Learning in a Random World》的合著者。Shafer的其他著作包括《A Mathematical Theory of Evidence》和《The Art of Causal Conjecture》。