| ISBN13: | 9781032863511 |
| ISBN10: | 103286351X |
| Kötéstípus: | Keménykötés |
| Terjedelem: | 342 oldal |
| Méret: | 246x174 mm |
| Súly: | 789 g |
| Nyelv: | angol |
| Illusztrációk: | 29 Illustrations, black & white; 29 Line drawings, black & white |
| 692 |
Arbitrage and Rational Decisions
GBP 89.99
Kattintson ide a feliratkozáshoz
A Prosperónál jelenleg nincsen raktáron.
This unique book offers a new approach to the modeling of rational decision making under conditions of uncertainty and strategic and competition interactions among agents.
This book presents a unified theory of rational decision-making under conditions of uncertainty and strategic and competitive interactions among agents. Its most fundamental axiom of rationality is the principle of no-arbitrage, namely that neither an individual decision maker nor a small group of game players nor a large group of market participants should behave in such a way as to provide a riskless profit opportunity to an outside observer. This principle provides a foundation for classic models of subjective probability and expected utility theory, state-preference theory, asset pricing theory, and cardinal welfare theory, and it provides tractable pathways for their generalization. Basic tools from finance (arbitrage pricing and risk-neutral probabilities) are shown to have wider applications, including models of non-expected-utility preferences and solution concepts for noncooperative games.
A central theme is that, notwithstanding the field?s expansion over the last several decades toward new and more sophisticated methods for quantifying the psychology of economic decisions (particularly with regard to ambiguity), the language of money remains fundamental for numerically precise cognition, interpersonal communication, common knowledge of preferences, and aggregation of beliefs. It also provides an obvious standard of economic rationality that applies equally to individuals and groups: don?t throw it away or allow your pocket to be picked.
The monetary environment provides an elementary setting for studying foundational issues such as the finiteness and imprecision of behavioral measurements, intrinsic incompleteness of preferences, interpersonal observability of preferences, perturbation of beliefs by attempts to measure them, separability of beliefs and tastes, effects of unobserved prior stakes in events, state-dependent utility for outcomes, and source-dependence of aversion to uncertainty. What is or is not possible here provides some perspective on what may happen in settings where objects of choice are less concrete or higher-dimensional or more personal in nature.
One of the book's key contributions is to show how noncooperative game theory can be directly unified with Bayesian decision theory and financial market theory without introducing separate notions of strategic rationality. The no-arbitrage requirement leads straight to the conclusion that correlated equilibrium rather than Nash equilibrium is the fundamental solution concept, and risk-neutral probabilities have a role to play in modeling uncertainty aversion in this setting.
The book also provides some history of developments in the field over the last century, emphasizing universal themes as well as controversies and paradigm shifts.
Robert Nau is a Professor Emeritus of Business Administration in the Fuqua School of Business, Duke University. He received his Ph.D. in Operations Research from the University of California at Berkeley. His research deals with mathematical models of decision-making under uncertainty, and his papers have been published in journals such as Operations Research, Management Science, Annals of Statistics, Journal of Economic Theory, and the International Journal of Game Theory. Throughout his career he taught a Ph.D. course on rational choice theory that drew students from other departments and schools at Duke University, as well as graduate courses in decision modeling and statistical forecasting.
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, risk aversion, and risk-neutral probabilities
6.1 The state-preference framework for choice under uncertainty
6.2 Examples of utility functions for risk-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 risk premium measure
6.7 Risk-neutral probabilities and the Slutsky matrix
7 Ambiguity and source-dependent risk 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 3x3 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
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 vsNash 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 Source-dependent utility and ambiguity 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 for arbitrage in expected utility theory
11.3 LP model for 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
Index
