Decision Making in Phantom Spaces

39 Pages Posted: 24 Oct 2011 Last revised: 5 Mar 2012

See all articles by Yehuda (Yud) Izhakian

Yehuda (Yud) Izhakian

City University of New York, Baruch College - Zicklin School of Business - Department of Economics and Finance

Zur Izhakian

University of Aberdeen

Date Written: March 4, 2009

Abstract

The phantom space, with its phantom probability measure, allows the framing of ambiguous probabilities of events, as well as their vague consequences. This paper introduces a decision-making model under uncertainty, established on a phantom generalization of the von Neumann-Morgenstern axiomatization. Beliefs in our model are subjective variations of objective probabilities, recorded in a framework comprising not only risk but also phantom effects. Uncertainty measures are carried over naturally into this setting such that many of the familiar attributes of objective probabilities are preserved. The degree of uncertainty, which is determined by the available information and subjective beliefs of the decision maker, is distinguished from the attitude toward uncertainty, which is drawn from her preferences. Decision making under ambiguity is a special case of our model in which probabilities are vague but outcomes of events are clearly forecasted. The Ellsberg paradox and an insurance dilemma are the main examples we present.

Keywords: Phantom probability measure, Phantom spaces, Decision making, Subjective probability, Risk, Ambiguity, Uncertainty, Ellsberg paradox

JEL Classification: C65, D81, D83

Suggested Citation

Izhakian, Yehuda (Yud) and Izhakian, Zur, Decision Making in Phantom Spaces (March 4, 2009). Available at SSRN: https://ssrn.com/abstract=1329366 or http://dx.doi.org/10.2139/ssrn.1329366

Yehuda (Yud) Izhakian (Contact Author)

City University of New York, Baruch College - Zicklin School of Business - Department of Economics and Finance ( email )

17 Lexington Avenue
New York, NY 10010
United States

HOME PAGE: http://people.stern.nyu.edu/yizhakia/

Zur Izhakian

University of Aberdeen ( email )

School of Law
Aberdeen
United Kingdom

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