### An S-linear State Preference Model

#### Abstract

We consider a situation in which there are n goods and an m-dimensional continuous infinity of states of the world. Without loss of generality, we assume that, in our model, the set of the states of the world is the m-dimensional real Euclidean space, and the set of the goods is the set of the first n positive integers. The first goal is the presence, in our model, of the analogous of the Arrow-Debreu ''contingent claims''. Using the canonical basis, we have that A(x) is an S-linear combination of the Dirac basis. So, for every portfolio x, the A-representation of x is an S-linear combination of the ''elementary securities'' represented by the elements of the canonical S-basis. This prove that the Dirac S-basis represents the analogous of the family of the Arrow-Debreu contingent claims.

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**DOI**: 10.1685 / CSC06037] About DOI[

**DOI**: 10.1685/] About DOI

Url Resolver: : http://dx.doi.org/10.1685/

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