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The Foundations of Probability with Black Swans
Author
Source
Journal of Probability and Statistics
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-03-21
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We extend the foundation of probability in samples with rare events that are potentially catastrophic, called black swans, such as natural hazards, market crashes, catastrophic climate change, and species extinction.
Such events are generally treated as ‘‘outliers’’ and disregarded.
We propose a new axiomatization of probability requiring equal treatment in the measurement of rare and frequent events—the Swan Axiom—and characterize the subjective probabilities that the axioms imply: these are neither finitely additive nor countably additive but a combination of both.
They exclude countably additive probabilities as in De Groot (1970) and Arrow (1971) and are a strict subset of Savage (1954) probabilities that are finitely additive measures.
Our subjective probabilities are standard distributions when the sample has no black swans.
The finitely additive part assigns however more weight to rare events than do standard distributions and in that sense explains the persistent observation of ‘‘power laws’’ and ‘‘heavy tails’’ that eludes classic theory.
The axioms extend earlier work by Chichilnisky (1996, 2000, 2002, 2009) to encompass the foundation of subjective probability and axiomatic treatments of subjective probability by Villegas (1964), De Groot (1963), Dubins and Savage (1965), Dubins (1975) Purves and Sudderth (1976) and of choice under uncertainty by Arrow (1971).
American Psychological Association (APA)
Chichilnisky, Graciela. 2010. The Foundations of Probability with Black Swans. Journal of Probability and Statistics،Vol. 2010, no. 2010, pp.1-11.
https://search.emarefa.net/detail/BIM-502189
Modern Language Association (MLA)
Chichilnisky, Graciela. The Foundations of Probability with Black Swans. Journal of Probability and Statistics No. 2010 (2010), pp.1-11.
https://search.emarefa.net/detail/BIM-502189
American Medical Association (AMA)
Chichilnisky, Graciela. The Foundations of Probability with Black Swans. Journal of Probability and Statistics. 2010. Vol. 2010, no. 2010, pp.1-11.
https://search.emarefa.net/detail/BIM-502189
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-502189