## Arbitrage, rationality, and equilibrium (1991)

Venue: | Theory and Decision |

Citations: | 7 - 0 self |

### BibTeX

@ARTICLE{Nau91arbitrage,rationality,,

author = {Robert F. Nau and Kevin F. Mccardle},

title = {Arbitrage, rationality, and equilibrium},

journal = {Theory and Decision},

year = {1991}

}

### OpenURL

### Abstract

ABSTRACT. No-arbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, no-arbitrage is synonymous with subjective expected utility maximization in personal decisions, competitive equilibria in capital markets and exchange economies, and correlated equilibria in noncooperative games. The arbitrage principle directly characterizes rationality at the market level; the appearance of deliberate optimization by individual agents is a consequence of their adaptation to the market. Concepts of equilibrium behavior in games and markets can thus be reconciled with the ideas that individual rationality is bounded, that agents use evolutionarily-shaped decision rules rather than numerical optimization algorithms, and that personal probabilities and utilities are inseparable and to some extent indeterminate. Risk-neutral probability distributions, interpretable as products of probabilities and marginal utilities, play a central role as observable quantities in economic systems.

### Citations

3572 |
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(Show Context)
Citation Context ... principle explicitly underlies the capital structure theorem (Modigliani and Miller 1958), the valuation of cash flows (Beja 1967, Rubinstein 1976, Ross 1978), and the pricing of assets and options (=-=Black and Scholes 1973-=-, Merton 1973, Ross 1976, Breeden and Litzenberger 1978, Brennan 1979). No-arbitrage is central to classical welfare economics, where it goes by the name of "Pareto optimality." In models of exchange ... |

2946 |
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Citation Context ...71) and Ellsberg (1961) are still a lively topic of debate; and the proposition that rationality is bounded by information-processing limitations (Simon 1955, 1976) or by evolutionary considerations (=-=Nelson and Winter 1982-=-) has given rise to a "behavioralist" countermovement in economics. (For a dialogue between rationalist and behavioralist views, see Hogarth and Reder 1986.) An enormous body of psychological research... |

1872 | The Foundations of Statistics - Savage - 1954 |

1242 |
Theory of Rational Option Pricing
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(Show Context)
Citation Context ...derlies the capital structure theorem (Modigliani and Miller 1958), the valuation of cash flows (Beja 1967, Rubinstein 1976, Ross 1978), and the pricing of assets and options (Black and Scholes 1973, =-=Merton 1973-=-, Ross 1976, Breeden and Litzenberger 1978, Brennan 1979). No-arbitrage is central to classical welfare economics, where it goes by the name of "Pareto optimality." In models of exchange economies, th... |

947 | Non-cooperative Games - Nash - 1951 |

904 |
A behavioral model of rational choice
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(Show Context)
Citation Context ...ing "paradoxes" first pointed out by Allais (1953, 1971) and Ellsberg (1961) are still a lively topic of debate; and the proposition that rationality is bounded by information-processing limitations (=-=Simon 1955-=-, 1976) or by evolutionary considerations (Nelson and Winter 1982) has given rise to a "behavioralist" countermovement in economics. (For a dialogue between rationalist and behavioralist views, see Ho... |

816 | Statistical reasoning with imprecise probabilities - Walley - 1991 |

588 | Games with Incomplete Information Played by ’Bayesian’ Players Part II
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Citation Context ...mes because it precisely captures the idea that Bayesian rationality on the part of all players will be common knowledge in every outcome of the game, provided that one accepts the Harsanyi doctrine (=-=Harsanyi 1967-=-) of homogenous prior beliefs. Support for Aumann's claim is provided by Nau and McCardle (1990) who show that the objective correlated equilibrium concept follows from a no-arbitrage argument- essent... |

588 |
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(Show Context)
Citation Context ...apital structure theorem (Modigliani and Miller 1958), the valuation of cash flows (Beja 1967, Rubinstein 1976, Ross 1978), and the pricing of assets and options (Black and Scholes 1973, Merton 1973, =-=Ross 1976-=-, Breeden and Litzenberger 1978, Brennan 1979). No-arbitrage is central to classical welfare economics, where it goes by the name of "Pareto optimality." In models of exchange economies, the relation ... |

517 | The Valuation of Options for Alternative Stochastic Processes
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(Show Context)
Citation Context ...s seems to contradict the notion of a risk-return tradeoff, the very hallmark of prudent investment, and this has led to the somewhat misleading characterization of such results as "preference free" (=-=Cox and Ross 1976-=-). The contradiction disappears if ~- is interpreted not as the "true" distribution of the representative agent, but as the (renormalized) product of her true probabilities and marginal utilities (Bej... |

402 | Theory of Value - Debreu - 1959 |

389 | Le Comportement de l’Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l’Ecole Américaine - Allais - 1953 |

389 |
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Citation Context ...cture theorem (Modigliani and Miller 1958), the valuation of cash flows (Beja 1967, Rubinstein 1976, Ross 1978), and the pricing of assets and options (Black and Scholes 1973, Merton 1973, Ross 1976, =-=Breeden and Litzenberger 1978-=-, Brennan 1979). No-arbitrage is central to classical welfare economics, where it goes by the name of "Pareto optimality." In models of exchange economies, the relation between arbitrage and competiti... |

352 | Risk, ambiguity, and the Savage axioms,” Quarterly - Ellsberg - 1961 |

324 | Correlated Equilibrium as an Expression of Bayesian Rationality - Aumann - 1987 |

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Citation Context ... The assumption that beliefs and preferences are completely ordered has been rejected by many decision theorists and philosophers (e.g., Koopman 1940, Good 1962, Smith 1961, Aumann 1962, Suppes 1974, =-=Levi 1980-=-); the decision-making "paradoxes" first pointed out by Allais (1953, 1971) and Ellsberg (1961) are still a lively topic of debate; and the proposition that rationality is bounded by information-proce... |

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Citation Context ...rguments over the foundations of subjective expected utility (e.g, Yaari 1985, Seidenfeld 1988). In the finance literature, the arbitrage principle explicitly underlies the capital structure theorem (=-=Modigliani and Miller 1958-=-), the valuation of cash flows (Beja 1967, Rubinstein 1976, Ross 1978), and the pricing of assets and options (Black and Scholes 1973, Merton 1973, Ross 1976, Breeden and Litzenberger 1978, Brennan 19... |

151 | Foundations for Financial Economics - Huang, Litzenberger - 1988 |

144 | Theory of Probability - DeFinetti - 1979 |

132 |
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Citation Context ...es support for the most important concepts of equilibrium in games and markets, but with weaker information requirements. It is consistent with "procedural" or "cognitive" views of rationality (e.g., =-=Simon 1976-=-; Munier 1991) which emphasize that the information-processing capabilities of the individual are finite and tailored to the specific demands of her physical and cultural environment. The competitive ... |

107 |
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(Show Context)
Citation Context ... is given by Nau 1991b.) As an example consider the capital budgeting problem whose decision tree is shown in Figure 5. (This is adapted from an example given by Trigeorgis and Mason and also used by =-=Copeland et al. 1990-=-.) The corporation has an opportunity to invest in a new plant whose returns depend on an uncertain state of the world, which will be "good" with probability p or "bad" with probability 1-p (as assess... |

100 | On the theory of syndicates - Wilson - 1968 |

75 | Arbitrage and Equilibrium in Economies with Infinitely Many Commodities - Kreps - 1981 |

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A Simple Approach to the Valuation of Risky Streams
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(Show Context)
Citation Context ...eld 1988). In the finance literature, the arbitrage principle explicitly underlies the capital structure theorem (Modigliani and Miller 1958), the valuation of cash flows (Beja 1967, Rubinstein 1976, =-=Ross 1978-=-), and the pricing of assets and options (Black and Scholes 1973, Merton 1973, Ross 1976, Breeden and Litzenberger 1978, Brennan 1979). No-arbitrage is central to classical welfare economics, where it... |

74 | An Extension of the Basic Theorems of Classical Welfare Economics - Arrow - 1951 |

48 |
Utility theory without the completeness axiom
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(Show Context)
Citation Context ...eans universally accepted. The assumption that beliefs and preferences are completely ordered has been rejected by many decision theorists and philosophers (e.g., Koopman 1940, Good 1962, Smith 1961, =-=Aumann 1962-=-, Suppes 1974, Levi 1980); the decision-making "paradoxes" first pointed out by Allais (1953, 1971) and Ellsberg (1961) are still a lively topic of debate; and the proposition that rationality is boun... |

47 | Coherent behavior in noncooperative games - Nau, McCardle - 1990 |

45 |
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(Show Context)
Citation Context ...ew of economic rationality is by no means universally accepted. The assumption that beliefs and preferences are completely ordered has been rejected by many decision theorists and philosophers (e.g., =-=Koopman 1940-=-, Good 1962, Smith 1961, Aumann 1962, Suppes 1974, Levi 1980); the decision-making "paradoxes" first pointed out by Allais (1953, 1971) and Ellsberg (1961) are still a lively topic of debate; and the ... |

44 | Separating probability elicitation from utilities - Kadane, Winkler - 1988 |

43 |
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(Show Context)
Citation Context ...l probabilities for the relevant events might be obtainable from observed prices of securities, commodities, and contingent claims. In the corporate finance literature, it has been asserted (e.g., by =-=Banz and Miller 1978-=- and Trigeorgis and Mason 1987) that "contingent claims analysis" based on risk-neutral probabilities is superior to conventional discounted cash flow analysis or decision tree analysis in this contex... |

40 |
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(Show Context)
Citation Context ... rationality is by no means universally accepted. The assumption that beliefs and preferences are completely ordered has been rejected by many decision theorists and philosophers (e.g., Koopman 1940, =-=Good 1962-=-, Smith 1961, Aumann 1962, Suppes 1974, Levi 1980); the decision-making "paradoxes" first pointed out by Allais (1953, 1971) and Ellsberg (1961) are still a lively topic of debate; and the proposition... |

32 |
Valuing Managerial Flexibility
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(Show Context)
Citation Context ...elevant events might be obtainable from observed prices of securities, commodities, and contingent claims. In the corporate finance literature, it has been asserted (e.g., by Banz and Miller 1978 and =-=Trigeorgis and Mason 1987-=-) that "contingent claims analysis" based on risk-neutral probabilities is superior to conventional discounted cash flow analysis or decision tree analysis in this context. In this section we examine ... |

30 | Thermodynamics - Callen - 1960 |

28 |
The measurement of belief
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(Show Context)
Citation Context ...lly accepted. The assumption that beliefs and preferences are completely ordered has been rejected by many decision theorists and philosophers (e.g., Koopman 1940, Good 1962, Smith 1961, Aumann 1962, =-=Suppes 1974-=-, Levi 1980); the decision-making "paradoxes" first pointed out by Allais (1953, 1971) and Ellsberg (1961) are still a lively topic of debate; and the proposition that rationality is bounded by inform... |

27 | J.(1987): Arbitrage and the Existence of Competitive Equilibrium - Werner |

26 | The arbitrage principle in financial economics - Varian - 1987 |

21 |
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Citation Context ...regation formulas for means and covariances are obtained in the absence of contingent claims markets-i.e., when agents' wealth distributions are required to be linear in the primary security returns (=-=Lintner 1969-=-) - although the market risk-neutral distribution is not directly observable in this case. More general aggregation formulas based on the exponential utility assumption, incorporating arbitrary probab... |

20 |
Bayes’ Method for Bookies
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(Show Context)
Citation Context ...bility" or "Dutch book") arguments based on de Finetti's theorem were used by Bayesian statisticians in the 1960's and 1970's to demonstrate the illogicality of frequentist statistical methods (e.g., =-=Freedman and Purves 1969-=-, Cornfield 1969, Lindley 1972, Heath and Sudderth 1972, Pierce 1973), his operational concept of probability was largely overshadowed by Savage's (1954) joint axiomatization of subjective probability... |

15 |
Decision theory without independence or without ordering: What is the difference
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(Show Context)
Citation Context ...ced in debates between frequentist and Bayesian statisticians in the 1960's and 1970's, and has emerged again in recent arguments over the foundations of subjective expected utility (e.g, Yaari 1985, =-=Seidenfeld 1988-=-). In the finance literature, the arbitrage principle explicitly underlies the capital structure theorem (Modigliani and Miller 1958), the valuation of cash flows (Beja 1967, Rubinstein 1976, Ross 197... |

10 |
The Bayesian outlook and its application
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(Show Context)
Citation Context ...rguments based on de Finetti's theorem were used by Bayesian statisticians in the 1960's and 1970's to demonstrate the illogicality of frequentist statistical methods (e.g., Freedman and Purves 1969, =-=Cornfield 1969-=-, Lindley 1972, Heath and Sudderth 1972, Pierce 1973), his operational concept of probability was largely overshadowed by Savage's (1954) joint axiomatization of subjective probability and expected ut... |

8 |
Bayesian Statistics: A Review, Society for
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(Show Context)
Citation Context ...n de Finetti's theorem were used by Bayesian statisticians in the 1960's and 1970's to demonstrate the illogicality of frequentist statistical methods (e.g., Freedman and Purves 1969, Cornfield 1969, =-=Lindley 1972-=-, Heath and Sudderth 1972, Pierce 1973), his operational concept of probability was largely overshadowed by Savage's (1954) joint axiomatization of subjective probability and expected utility in terms... |

7 | The interrelations of finance and economics: Theoretical perspectives. American Economic Review 77:29–34 - Ross - 1987 |

5 | Valuation equilibrium and pareto - Debreu - 1954 |

4 | Subjectivity and Correlation in Randomized - Aumann - 1974 |

4 | Decision Analysis: Practice and - Howard - 1988 |

3 |
On Some Difficulties in a Frequency Theory of Inference,” The
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(Show Context)
Citation Context ...esian statisticians in the 1960's and 1970's to demonstrate the illogicality of frequentist statistical methods (e.g., Freedman and Purves 1969, Cornfield 1969, Lindley 1972, Heath and Sudderth 1972, =-=Pierce 1973-=-), his operational concept of probability was largely overshadowed by Savage's (1954) joint axiomatization of subjective probability and expected utility in terms of binary preferences. The lack of pr... |

3 | 1961]: ‘Consistency in Statistical Inference and Decision - Smith |

2 |
Capital markets with delayed learning
- Beja
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(Show Context)
Citation Context ...ty (e.g, Yaari 1985, Seidenfeld 1988). In the finance literature, the arbitrage principle explicitly underlies the capital structure theorem (Modigliani and Miller 1958), the valuation of cash flows (=-=Beja 1967-=-, Rubinstein 1976, Ross 1978), and the pricing of assets and options (Black and Scholes 1973, Merton 1973, Ross 1976, Breeden and Litzenberger 1978, Brennan 1979). No-arbitrage is central to classical... |

1 | Les Throries de l'Equilibre Economique Grnrral et de l'Efficacit6 Maximale: Impasses Rrcents et Nouvelles Perspectives', Revue d'Economie Politique, May-June - Allais - 1971 |

1 |
The Pricing of Contingent Claims in Discrete Time Markets
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(Show Context)
Citation Context ...iller 1958), the valuation of cash flows (Beja 1967, Rubinstein 1976, Ross 1978), and the pricing of assets and options (Black and Scholes 1973, Merton 1973, Ross 1976, Breeden and Litzenberger 1978, =-=Brennan 1979-=-). No-arbitrage is central to classical welfare economics, where it goes by the name of "Pareto optimality." In models of exchange economies, the relation between arbitrage and competitive equilibrium... |