Monotone Risk Aversion
AbstractThis paper shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with a positive and absolutely continuous derivative. The cumulative absolute risk aversion function, which is defined as the negative of the logarithm of the marginal utility, will also be absolutely continuous. Its density, called the absolute risk aversion density, is a generalization of the coefficient of absolute risk aversion, and it is well defined almost everywhere. A strictly increasing and risk averse utility function has decreasing absolute risk aversion if, and only if, it has a decreasing absolute risk aversion density and if, and only if, the cumulative absolute risk aversion function is increasing and concave. This leads to a convenient characterization of all such utility functions. Analogues of all the results also hold for increasing absolute risk aversion, as well as for increasing and decreasing relative risk aversion.
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Bibliographic InfoPaper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 1651.
Date of creation: May 1997
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- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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- Würth, Andreas & Schumacher, J.M., 2011.
"Risk aversion for nonsmooth utility functions,"
Journal of Mathematical Economics,
Elsevier, vol. 47(2), pages 109-128, March.
- Frank Hansen, 2006. "Decreasing Relative Risk Premium," Discussion Papers 06-21, University of Copenhagen. Department of Economics.
- Li, Minqiang, 2013. "On Aumann and Serrano's Economic Index of Risk," MPRA Paper 47466, University Library of Munich, Germany.
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