Arbitrage and Rational Decisions

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
1. Introduction
	1.1. Social physics
	1.2. The importance of having money
	1.3. The impossibility of measuring beliefs
	1.4. Risk-neutral probabilities
	1.5. No-arbitrage as common knowledge of rationality
	1.6. A road map of the book
2. Preference axioms, fixed points, and separating hyperplanes
	2.1. The axiomatization of probability and utility
	2.2. The independence axiom
	2.3. The difficulty of measuring utility
	2.4. The fixed point theorem
	2.5. The separating hyperplane theorem
	2.6. Primal/dual linear programs to search for arbitrage opportunities
	2.7. No-arbitrage and the fundamental theorems of rational choice
3. Subjective probability
	3.1. Elicitation of beliefs
	3.2. A 3-state example of probability assessment
	3.3. The fundamental theorem of subjective probability
	3.4. Bayes’ theorem and (not) learning over time
	3.5. Incomplete preferences and imprecise probabilities
	3.6. Continuous probability distributions
	3.7. Prelude to game theory: no-ex-post-arbitrage and zero probabilities
4. Expected utility
	4.1. Elicitation of tastes
	4.2. The fundamental theorem of expected utility
	4.3. Continuous payoff distributions and measurement of risk aversion
	4.4. The fundamental theorem of utilitarianism (social aggregation)
5. Subjective expected utility
	5.1. Joint elicitation of beliefs and tastes
	5.2. The fundamental theorem of subjective expected utility
	5.3. (In)separability of beliefs and tastes (state-dependent utility)
	5.4. Incomplete preferences with state-dependent utilities
	5.5. Representation by sets of probability/utility pairs
6. State-preference theory, uncertainty aversion, and risk-neutral probabilities
	6.1. The state-preference framework for choice under uncertainty
	6.2. Examples of utility functions for uncertainty-averse agents
	6.3. The fundamental theorem of state-preference theory
	6.4. Risk-neutral probabilities and their matrix of derivatives
	6.5. The risk aversion matrix
	6.6. A generalized uncertainty premium measure
	6.7. Risk-neutral probabilities and the Slutsky matrix
7. Ambiguity and source-dependent uncertainty aversion
	7.1. Introduction
	7.2. Ellsberg’s paradox and smooth non-expected-utility preferences
	7.3. Source-dependent utility revealed by risk-neutral probabilities
	7.4. A 3 × 3 example of a two-source model
	7.5. The second-order-uncertainty smooth model
	7.6. Discussion
	7.7. Some history of non-expected-utility theory
8. Noncooperative games
	8.1. Introduction
	8.2. Solution of a 1-player game by no-arbitrage
	8.3. Solution of a 2-player game by no-arbitrage
	8.4. Games of coordination: chicken, battle of the sexes, and stag hunt
	8.5. An overview of correlated equilibrium and its properties
	8.6. The fundamental theorem of noncooperative games
	8.7. Examples of Nash and correlated equilibria
	8.8. Correlated equilibrium vs. Nash equilibrium and rationalizability
	8.9. Risk aversion and risk-neutral equilibria
	8.10. Playing a new game
	8.11. Games of incomplete information
	8.12. Discussion
9. Asset pricing
	9.1. Introduction
	9.2. Risk-neutral probabilities and the fundamental theorem
	9.3. The multivariate normal/exponential/quadratic model
	9.4. Market aggregation of means and covariances
	9.5. The subjective capital asset pricing model (CAPM)
10. Summary of the fundamental theorems and models
	10.1. Perspectives on the foundations of rational choice theory
	10.2. Axioms for preferences and acceptable bets
	10.3. Subjective probability theory
	10.4. Expected utility theory
	10.5. Subjective expected utility theory
	10.6. State-preference theory and risk-neutral probabilities
	10.7. Ambiguity and source-dependent uncertainty aversion
	10.8. Noncooperative game theory
	10.9. Asset pricing theory
11. Linear programming models for seeking arbitrage opportunities
	11.1. LP models for arbitrage in subjective probability theory
	11.2. LP model for arbitrage in expected utility theory
	11.3. LP model for arbitrage in subjective expected utility theory
	11.4. LP model for ex-post-arbitrage and correlated equilibria in games
	11.5. LP model for arbitrage in asset pricing theory
12. Selected proofs
Bibliography
Author Index
Subject Index