The Foundations of Uncertainty with Black Swans

Graciela Chichilnisky

A chapter in The Economics of the Global Environment, 2016, pp 117-128 from Springer

Abstract: Abstract We extend the foundation of subjective probability to integrate rare events that are potentially catastrophic, called black swans, such as natural hazards, market crashes, catastrophic climate change and major episodes of species extinction. Such events are generally treated as ‘outliers’ and often disregarded. We propose a new axiomatization of subjective probability requiring equal treatment for 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 (1972) 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 in Chichilnisky (2000; 2002) to encompass the foundation of subjective probability, and axiomatic treatments of subjective probability by Savage (1972), Villegas (1964) and the foundations of choice under uncertainty in Arrow (1971).

Keywords: Black Swan; Finitely Additive Measures; Chichilnisky; Countable Additivity; Subjective Probability (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:steccp:978-3-319-31943-8_6

Ordering information: This item can be ordered from
http://www.springer.com/9783319319438

DOI: 10.1007/978-3-319-31943-8_6

Access Statistics for this chapter

More chapters in Studies in Economic Theory from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().