In this Supplement we provide foundations for the asset structures used in the main part of the paper, as well as in Appendix A. We use results by Choquet (1966), Kendall (1962) and Polyrakis (1999) to demonstrate how these asset structures can be generated from a general set of assets available in the economy and a general set of financial constraints. A sufficient condition called "internal completeness" is for the set of assets to contain an appropriate set of put and call options so that the implied set of payoffs is a sublattice of the Euclidean space.