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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Application of operator monotone functions in economics; pp. 42–47

(Full article in PDF format) doi: 10.3176/proc.2010.1.07


Authors

Frank Hansen

Abstract

Operator monotone functions play an important role in economics. We show that 2-monotonicity is equivalent to decreasing relative risk premium, a notion recently introduced in microeconomics. We also show that an operator monotone function is risk vulnerable, a notion introduced by Gollier and Pratt.

Keywords

mathematical economics, operator monotone function, relative risk premium, risk vulnerability, utility function.

References

1. Bernoulli , D. Specimen theoriae novae de mensura sortis. Commentarii Academiae Scientiarum Imperialis Petropolitanae , 1738. Translation: Bernoulli , D. Exposition of a new theory on the measurement of risk. Econometrica , 1954 , 22 , 23–36.
doi:10.2307/1909829

2. Ellsberg , D. Risk , ambiguity , and the Savage axioms. Quart. J. Econ. , 1961 , 75 , 643–669.
doi:10.2307/1884324

3. Gollier , G. and Pratt , J. Risk vulnerability and the tempering effect of background risk. Econometrica , 1996 , 64 , 1109–1123.
doi:10.2307/2171958

4. Hansen , F. Decreasing relative risk premium. B.E. J. Theor. Econ. , 2007 , 7(1) (Topics) , Article 37.

5. Knight , F. H. Risk , Uncertainty and Profit. Houghton Mifflin , Boston , 1921.

6. Löwner , K. Über monotone Matrixfunktionen. Math. Z. , 1934 , 38 , 177–216.
doi:10.1007/BF01170633

7. Savage , L. The Foundations of Statistics. John Wiley , New York , 1954.
 
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Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
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