Game-theoretic foundations for probabili
โ Shafer, Glenn; Vovk, Vladimir
๐ Library
๐
2019
๐ John Wiley & Sons
๐ English
โฆ LIBER โฆ
๐
Game-theoretic foundations for probability and finance
โ Scribed by Shafer G., Vovk V
- Publisher
- Wiley
- Year
- 2019
- Tongue
- English
- Leaves
- 474
- Category
- Library
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โฆ Table of Contents
Cover......Page 1
WILEY SERIES IN PROBABILITY AND STATISTICS......Page 3
Game-TheoreticFoundations for Probabilityand Finance......Page 4
ยฉ 2019......Page 5
Contents......Page 6
Preface......Page 12
Acknowledgments......Page 16
Part I: Examples in Discrete Time......Page 18
1 Borelโs Law of LargeNumbers......Page 24
2 Bernoulliโs and DeMoivreโs Theorems......Page 50
3 Some BasicSupermartingales......Page 73
4 Kolmogorovโs Law of LargeNumbers......Page 87
5 The Law of the IteratedLogarithm......Page 110
Part II: Abstract Theory in DiscreteTime......Page 126
6 Betting on a SingleOutcome......Page 128
7 Abstract Testing Protocols......Page 151
8 Zero-One Laws......Page 173
9 Relation to Measure-Theoretic Probability......Page 190
Part III: Applications in DiscreteTime......Page 210
10 Using Testing Protocols inScience and Technology......Page 212
11 Calibrating Lookbacks andp-Values......Page 244
12 Defensive Forecasting......Page 267
Part IV: Game-Theoretic Finance......Page 319
13 Emergence of Randomnessin Idealized FinancialMarkets......Page 323
14 A Game-Theoretic ItรดCalculus......Page 352
15 Numeraires in MarketSpaces......Page 384
16 Equity Premium and CAPM......Page 397
17 Game-Theoretic PortfolioTheory......Page 415
Terminology and Notation......Page 430
List of Symbols......Page 436
References......Page 439
Index......Page 465
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