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- Title
Differentiable von Neumann-Morgenstern utility.
- Authors
Nielsen, Lars Tyge
- Abstract
Differentiability is a convenient property of von Neumann-Morgenstern utility functions which is almost always imposed but has not been translated into behavioral terms. In applications, expected utility is usually maximized subject to a constraint, and the maximization is carried out by differentiating the utility function. This paper presents two sets of necessary and sufficient conditions for a risk averse von Neumann-Morgenstern utility function to be differentiable. The first of them is formulated in terms of the equivalent risk premia of small gambles. It says, in brief, that the equivalent risk premium is of a smaller order of magnitude than the risk itself, as measured by the expectation of the absolute value of the risk. The second set of necessary and sufficient conditions is formulated in terms of the probability premium of small lotteries. It says, essentially, that the probability premium for small binary lotteries goes to zero as the size of the lottery goes to zero.
- Subjects
EXPECTED utility; UTILITY theory; RISK premiums; PROBABILITY theory; RISK aversion
- Publication
Economic Theory, 1999, Vol 14, Issue 2, p285
- ISSN
0938-2259
- Publication type
Article
- DOI
10.1007/s001990050294