Arbitrage and Rational Decisions

Robert Nau

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English

Chapman & Hall/CRC
16 December 2024

Economics; Probability & statistics; Game theory; Applied mathematics

Series: Chapman and Hall/CRC Financial Mathematics Series

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 presentsa unified theory in whichthemost basic axiom ofrationality istheprincipleofno-arbitrage,namelythatneitheranindividualdecisionmakernorasmallgroup of strategiccompetitorsnora largegroupofmarket participantsshould behaveinsuch a wayasto providearisklessprofitopportunitytoanoutsideobserver.

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.

By: Robert Nau
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 246mm, Width: 174mm,
ISBN: 9781032863511
ISBN 10: 103286351X
Series: Chapman and Hall/CRC Financial Mathematics Series
Pages: 352
Publication Date: 16 December 2024
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming

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. Professor Nau is an internationally known authority on mathematical models of decision making under uncertainty. His research has been supported by the National Science Foundation, 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. He was a co-recipient of the Decision Analysis Society Best Publication Award. One of the themes in Professor Nau’s research is that models of rational decision making in various fields are linked by a single unifying principle, namely the principle of no-arbitrage, i.e., avoiding sure loss at the hands of a competitor. This principle is central to modern finance theory, but it can also be shown to be the fundamental rationality concept that underlies Bayesian statistics, decision analysis, and game theory. Professor Nau has taught the core MBA courses on Decision Models and Statistics in several programs, and he developed an MBA elective course on Forecasting which he has taught throughout his career. He also teaches a course on Rational Choice Theory in the Ph.D. program that draws students from other departments and schools at Duke University.