Chichilnisky, Graciela (2017): The Topology of Change: Foundations of Probability with Black Swans. Published in: The Topology of Change: Foundations of Probability with Black Swans

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Abstract
Classic probability theory treats rare events as ‘outliers’ that are often disregarded and underestimated. Yet in a moment of change rare events can become frequent and frequent events rare. We therefore postulate new axioms for probability theory that require a balanced treatment for rare and frequent events, based on what we call ”the topology of change”. The axioms extend the foundation of probability to integrate rare but potentially catastrophic events or black swans: natural hazards, market crashes, catastrophic climate change and major episodes of species extinction. The new results presented in this article include a characterization of a family of purely finitely additive measures that are  somewhat surprisingly  absolutely continuous with respect to the Lebesgue measure. This is a new development from an earlier characterization of all the probabilities measures implied by the new axioms as a combination of purely finitely additive and countably additive measures that was first established in Chichilnisky (2000, 2002, 2008, 2009), and the results are contrasted here to the work of Kolmogorov (1932), De Groot (1970), Arrow (1971)), Dubins and Savage (1963), Savage (1954), Von Neumann Morgernstern (1954), and Hernstein and Milnor (1972).
Item Type:  MPRA Paper 

Original Title:  The Topology of Change: Foundations of Probability with Black Swans 
English Title:  The Topology of Change: Foundations of Probability with Black Swans 
Language:  English 
Keywords:  Lebesgue Measure, Rare Event, Additive Measure, Frequent Event, Heavy Tail, additive measure, Classic probability, vanishing sequence , continuity axiom, the topology of change 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking 
Item ID:  86080 
Depositing User:  Graciela Chichilnisky 
Date Deposited:  31 Aug 2018 23:33 
Last Modified:  28 Sep 2019 21:27 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/86080 