Integrability of Demand in Incomplete Markets: Kreps-Porteus-Selden Preferences

Abstract

We provide necessary and sufficient conditions such that consumption and asset demands in an incomplete market setting can be rationalized by Kreps-Porteus-Selden preferences and provide a means for recovering the underlying unique representations of risk and time preferences. The incompleteness of asset markets introduces two serious problems in attempting to use the classic Slutsky symmetry and negative semideniteness properties employed in certainty demand analysis. First, contingent claim prices are not unique and second, they do not vary independently. Non-uniqueness is a key obstacle to rationalizing conditional asset demand by a representation of risk preferences. Non-independence precludes proving the existences of an overall Kreps-Porteus-Selden representation dened over consumption and contingent claims and hence the existence of a representation of time preferences. Mechanisms are provided for overcoming both obstacles.

Keywords: Kreps-Porteus-Selden preferences, expected utility, contingent claims, integrability, incomplete markets

JEL Classification: D01, D11, D80