Risk aversion in the theory of expected utility with rank dependent probabilities. (English) Zbl 0632.90007
This paper investigates risk aversion within an extended model of expected utility which has been axiomatized by M. Quiggin [J. Econ. Behav. Organ. 3 (1982)]. Let J be a real interval. A preference relation \(\gtrsim\) in the set of probability distribution functions F over J is represented by a functional
\[
V(F)=\int_{J}v(z)d(g\circ F)(z)
\]
where v and g are continuous, strictly increasing functions, \(v: J\to {\mathbb{R}}\) and g: [0,1]\(\to [0,1]\) onto. Notions of risk aversion are introduced which are similar to the Arrow-Pratt notions in classical expected utility. Provided the functionals V are Gateaux differentiable, it is shown that a preference relation is more risk averse than another preference relation \(\gtrsim^*\) iff v and g are concave transforms of \(v^*\) and \(g^*\), respectively. Results on the (conditional) demand for a riskless asset and on diversification are derived which partly correspond to the classical ones and partly differ from them.
Reviewer: K.Mosler
MSC:
| 91B16 | Utility theory |
| 91B08 | Individual preferences |
| 60A05 | Axioms; other general questions in probability |
Keywords:
rank dependent probabilities; conditional asset demand; risk aversion; expected utility; Gateaux differentiableReferences:
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