Generally accepted observable behavior has led to the following classes of continuously differentiable utility functions, u (•):
-
I.
Nonsatiation axiom: u′ > 0
-
II.
Risk aversion: u′ > 0, u″ < 0
Adopting the notation of (Bawa, 1975), let the uncertain prospects be characterized by random variables xi,i= 1,2,…,n+ 1, with known continuous probability distribution functions defined over an open interval R 1 given by (a, b),a >b.
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Bodurtha, J.N., Shen, Q. (2009). Normally Distributed Admissible Choices are Optimal. In: Brams, S.J., Gehrlein, W.V., Roberts, F.S. (eds) The Mathematics of Preference, Choice and Order. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79128-7_5
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