| ISBN13: | 9781032863511 |
| ISBN10: | 103286351X |
| Kötéstípus: | Keménykötés |
| Terjedelem: | 342 oldal |
| Méret: | 246x174 mm |
| Nyelv: | angol |
| Illusztrációk: | 29 Illustrations, black & white; 29 Line drawings, black & white |
| 700 |
Kombinatorika és gráfelmélet
Valószínűségelmélet és matematikai statisztika
Optimalizáció, lineáris programozás, játékelmélet
Alkalmazott matematika
Közgazdaságtan
Menedzsment, vállalatirányítás
Pénzügy, befektetés
Kombinatorika és gráfelmélet (karitatív célú kampány)
Valószínűségelmélet és matematikai statisztika (karitatív célú kampány)
Optimalizáció, lineáris programozás, játékelmélet (karitatív célú kampány)
Alkalmazott matematika (karitatív célú kampány)
Közgazdaságtan (karitatív célú kampány)
Menedzsment, vállalatirányítás (karitatív célú kampány)
Pénzügy, befektetés (karitatív célú kampány)
Arbitrage and Rational Decisions
GBP 74.99
Kattintson ide a feliratkozáshoz
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 unique book offers a new approach to the modeling of rational decision-making under conditions of uncertainty and strategic and competition interactions among agents. It presents a unified theory in which the most basic axiom of rationality is the principle of no-arbitrage, namely that neither an individual decision maker nor a small group of strategic competitors nor a large group of market participants should behave in such a way as to provide a riskless profit opportunity to an outside observer.
Both those who work in the finance area and those who work in decision theory more broadly will be interested to find that basic tools from finance (arbitrage pricing and risk-neutral probabilities) have broader applications, including the modeling of subjective probability and expected utility, incomplete preferences, inseparable probabilities and utilities, nonexpected utility, ambiguity, noncooperative games, and social choice. Key results in all these areas can be derived from a single principle and essentially the same mathematics.
A number of insights emerge from this approach. One is that the presence of money (or not) is hugely important for modeling decision behavior in quantitative terms and for dealing with issues of common knowledge of numerical parameters of a situation. Another is that beliefs (probabilities) do not need to be uniquely separated from tastes (utilities) for the modeling of phenomena such as aversion to uncertainty and ambiguity. Another over-arching issue is that probabilities and utilities are always to some extent indeterminate, but this does not create problems for the arbitrage-based theories.
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 assumptions about strategic rationality. This leads to the conclusion that correlated equilibrium rather than Nash equilibrium is the fundamental solution concept.
The book is written to be accessible to advanced undergraduates and graduate students, researchers in the field, and professionals.
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
