Mathematical Economics and Finance II

Incomplete markets: Radner existence theorem, generic existence, indetermination of equilibrium.General equilibrium with infinitely many goods: Bewley’s theorem, properties of preferences, equilibrium in Banach lattices (Mas-Colell’s Theorem). Equilibrium in finance: separable utilities. Other topics in general equilibrium: differential approach, local uniqueness, aggregation theorems, and Soinnenschein-Mantel-Debreu’s Theorem.

References:
BEWLEY, T. – Existence of Equilibria in Economies with Infinitely Many Commodities, Journal of Economic Theory 4, 1972.
DEBREU, G. – Mathematical Economics, Twenty papers of Gerard Debreu, Econometric Society Monographs 4, Cambridge University Press, 1989.
MAGILL, M., SHAFER, W. – Incomplete Markets – Chapter 30, Handbook of Mathematical Economics, Vol. IV, ed. Hildenbrand and Sonnenschein. North Holland, Amsterdam, 1991.
MAS-COLELL, A., ZAME, W. – Equilibrium Theory in Infinite Dimensional Spaces, in: Handbook of Mathematical Economics vol. IV, ed. W. Hildenbrand e H. Sonneschein, North Holland, Amsterdam, 1991.

* Standard program. The teacher has the autonomy to make any changes