On the algebraic dimension of ''bad'' prices in incomplete markets with real assets (Q1892229)

The paper uses the tool introduced by \textit{M. J. P. Magill} and \textit{W. J. Shafer} [J. Math. Econ. 19, No. 1/2, 167-194 (1990; Zbl 0694.90019)] viz., the stratification of bad price sets and applies it to a two period exchange economy model with incomplete markets. The paper exhibits a generic good class of real asset structures that are independent of the economy, where the class is defined by means of the dimension of the critical prices as a semi algebraic set. This class also contains commodity forward contracts and all constant-rank asset structures. As a by product of this construction, it is deduced that there is no real asset structure for which a low rank viable financial market equilibrium exists. The algebraic nature of the construction allows one to conclude that the genericity argument can be independent of the nonfinancial fundamentals of the economy. Further, the stratification approach is shown to lead to stronger results for the case of real assets.