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- Robert F. Nau
- Management Science
- 2006

S expected utility theory does not distinguish between attitudes toward uncertainty (ambiguous probabilities) and attitudes toward risk (unambiguous probabilities). Both are explained in terms of nonlinear utility for money rather than properties of events per se, hence, the decision maker displays the same attitude toward all sources of risk and… (More)

- Victor Richmond R. Jose, Robert F. Nau, Robert L. Winkler
- Operations Research
- 2008

Information measures arise in many disciplines, including forecasting (where scoring rules are used to provide incentives for probability estimation), signal processing (where information gain is measured in physical units of relative entropy), decision analysis (where new information can lead to improved decisions), and finance (where investors optimize… (More)

- Victor Richmond R. Jose, Robert F. Nau, Robert L. Winkler
- Management Science
- 2009

S rules can provide incentives for truthful reporting of probabilities and evaluation measures for the probabilities after the events of interest are observed. Often the space of events is ordered and an evaluation relative to some baseline distribution is desired. Scoring rules typically studied in the literature and used in practice do not take account of… (More)

- Robert F. Nau, DE FINETTI
- 2002

De Finetti’s treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals. De Finetti defined subjective probabilities in terms of the rates at which individuals are willing to… (More)

- Robert F. Nau
- Management Science
- 2003

The Pratt-Arrow measure of local risk aversion is generalized for the n-dimensional state-preference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities, unobservable stochastic prior wealth, and/or smooth nonexpected-utility preferences. Local risk aversion is measured by the matrix of… (More)

- Robert F. Nau, Victor Richmond
- 2007

Suppose that a risk-averse expected utility maximizer with a precise probability distribution p bets optimally against a risk neutral opponent (or equivalently invests in an incomplete market for contingent claims) whose beliefs (or prices) are described by a convex setQ of probability distributions. This utilitymaximization problem is the dual of the… (More)

- Robert F. Nau
- 2005

This paper presents a new method of modeling indeterminate and incoherent probability judgments in decision analysis problems. The decision maker's degree of beliefs in the occurrence of an event is represented by a unimodal (in fact, concave) function on the unit interval, whose parameters are elicited in terms of lowcr and upper probabilities with… (More)

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… (More)

- Noncooperative Games, Robert F. Nau, Kevin F. McCardle
- 1990

A new concept of mutually expected rationality in noncooperative games is proposed: joint coherence. This is an extension of the “no arbitrage opportunities” axiom that underlies subjective probability theory and a variety of economic models. It sheds light on the controversy over the strategies that can reasonably be recommended to or expected to arise… (More)

- Robert F. Nau, Victor Richmond, Robert L. Winkler
- 2009

In this paper we model the problem faced by a riskaverse decision maker with a precise subjective probability distribution who bets against a risk-neutral opponent or invests in a financial market where the beliefs of the opponent or the representative agent in the market are described by a convex set of imprecise probabilities. The problem of finding the… (More)

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