The Foster-Hart Measure of Riskiness for General Gambles

24 Pages Posted: 31 Jan 2013

See all articles by Frank Riedel

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Tobias Hellmann

Bielefeld University - Center for Mathematical Economics

Date Written: January 3, 2013

Abstract

Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defi ning equation has no solution for many common continuous distributions including many uniform distributions, e.g. We show how to extend consistently the defi nition of riskiness to continuous random variables. For many continuous random variables, the risk measure is equal to the worst-case risk measure, i.e. the maximal possible loss incurred by that gamble. We also extend the Foster{Hart risk measure to dynamic environments for general distributions and probability spaces, and we show that the extended measure avoids bankruptcy in infi nitely repeated gambles.

Keywords: Risk Measures, Operational, Bankruptcy, Continuous Random Variable

JEL Classification: D81, G11

Suggested Citation

Riedel, Frank and Hellmann, Tobias, The Foster-Hart Measure of Riskiness for General Gambles (January 3, 2013). Institute of Mathematical Economics Working Paper No. 474, Available at SSRN: https://ssrn.com/abstract=2209231 or http://dx.doi.org/10.2139/ssrn.2209231

Frank Riedel (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Tobias Hellmann

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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