ABSTRACT
We consider a two-period economy, with the current and next period, respectively indexed by zero and one. Next-period uncertainty is represented by a finite number S, of states of nature, indexed by s, and by a probability distribution π assigning πs to every state s. A vector ðx0; x1Þ is used to specify a change in the current level of income (or consumption of a single commodity) x0 and a contingent claim x1 on date-one income. The space of all contingent claims X is a finite (topological) vector space endowed with the probability inner product, E½x� :¼Ps πsxs. We also assume that contingent claims have finite second moments, xk k :¼ ðE½x2�Þ1=2 <þ1 (i.e. X � L2). X is endowed with a natural ordering � , which defines the positive cone Xþ ¼ fx 2 X : x � 0g, and the strictly-positive cone Xþþ ¼ Xþnf0g.
