We present necessary and sufficient conditions on the asset span of incomplete derivative markets for insuring marketed portfolios. If the asset span is finite dimensional there exists a polynomial-time algorithm for deciding if every marketed portfolio is insurable, moreover this algorithm computes the minimum cost insurance portfolio.
In addition, we extend the Cox-Leland characterization of optimal portfolio insurance in complete derivative markets to asset spans of incomplete derivative markets where every marketed portfolio is insurable.
We present versions of the two fundamental welfare theorems of economics for exchange economies with a countable number of agents and an infinite dimensional commodity space. These results are then specialized to the overlapping generations model.
An Edgeworth equilibrium is an allocation that belongs to the core of every n-fold replica of the economy. In [2] we studied in the setting of Riesz spaces the properties of Edgeworth equilibria for pure exchange economies with infinite dimensional commodity spaces. In this work, we study the same problem for economies with production. Under some relatively mild conditions we establish (among other things) that: 1. Edgeworth equilibria exist; 2. Every Edgeworth equilibrium is a quasiequilibrium; and 3. An allocation is an Edgeworth equilibrium if and only if it can be “decentralized” by a price system.
JEL Classification: 021
Keywords: Edgeworth equilibrium, Riesz spaces, production economies
The paper studies pure exchange economies with infinite dimensional commodity spaces in the setting of Riesz dual systems. Several new concepts of equilibrium are introduced. An allocation (x1, …, xm) is said to be a) an Edgeworth equilibrium whenever it belongs to the core of every n-fold replication of the economy; and b) an ε-Walrasian equilibrium whenever for each ε > 0 there exists some price p not equal to 0 with p∙ω = 1 (where ω = Σωi is the total endowment) and with x ≥i xi implying p times x ≥ p∙ωi – ε. The major results of the paper are the following:
Theorem I: Edgeworth equilibria exist.
Theorem II: An allocation is an Edgeworth equilibrium if and only if it is an ε-Walrasian equilibrium.
Theorem III: If preferences are proper, then every Edgeworth equilibrium is a quasi-equilibrium.
The existence of equilibria is established in an overlapping generations exchange economy, where each generation lives for two periods and the commodity space is the positive cone of an infinite dimensional Riesz space. In particular, we establish the existence of equilibria in the stochastic overlapping generations model, i.e., we establish the existence of equilibria when the commodity space in each period is L∞ equipped with the Mackey topology τ(L∞, L1).