Complete and incomplete financial markets in multi-good economies

Ehling, P and Heyerdahl-Larsen, C (2015) Complete and incomplete financial markets in multi-good economies. Journal of Economic Theory, 160 (Dec). pp. 438-462. ISSN 0022-0531

Abstract

We investigate conditions for endogenous incompleteness and completeness in continuous-time financial markets driven by diffusion processes with multiple consumption goods and heterogeneous agents. We show that for a class of utility functions the financial market is endogenously incomplete. A sufficient condition for market completeness is that the dividend diffusion matrix in units of the numeraire good is invertible. Further, financial market completeness can depend on the choice of the numeraire good since changing the numeraire good implies a change of the risk-free asset and the asset structure.