Abstract

If we study the expected utility function then we deal with a unified approach to an integrated formulation of decision theory in its two subjective components: utility and probability. We decompose the expected utility function inside of an m-dimensional linear space after decomposing a contingent consumption plan viewed as a univariate random quantity. We propose a condition of coherence compatible with all possible attitudes in the face of risk of a consumer. It is a geometric condition of coherence. In particular, we consider a risk-neutral consumer and his coherent decisions under uncertainty. The right closed structure in order to deal with utility and probability is a linear space in which we study coherent decisions under uncertainty having as their goal the maximization of the prevision of the utility associated with a contingent consumption bundle.

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