Decisions in Economics and Finance

, Volume 35, Issue 1, pp 1–28 | Cite as

Risk aversion and risk vulnerability in the continuous and discrete case

A unified treatment with extensions
  • Martin Bohner
  • Gregory M. Gelles


This paper discusses utility functions for money, where allowable money values are from an arbitrary nonempty closed subset of the real numbers. Thus, the classical case, where this subset is a closed interval (bounded or not) of the real line, is included in the study. The discrete case, where this subset is the set of all integer numbers, is also included. In a sense, the discrete case (which has not been addressed in the literature thus far) is more suitable for real-world applications than the continuous case. In this general setting, the concepts of risk aversion and risk premium are defined, an analogue of Pratt’s fundamental theorem is proved, and temperance, prudence, and risk vulnerability are examined.


Utility function Time scale Delta derivative Risk aversion Risk vulnerability 

JEL Classification

C02 D81 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Economics, RollaMissouri University of Science and TechnologyMissouriUSA

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