Equilibrium and arbitrage in incomplete asset markets with fixed prices
type: Item
instance of: scholarly article
title: Equilibrium and arbitrage in incomplete asset markets with fixed prices
zbMATH Open document ID: 1044.91020
DOI: 10.1016/S0304-4068(02)00013-7
published in: Journal of Mathematical Economics
publication date: 2002-12-02T00:00:00Z
review text: An equilibrium existence theorem is established in a standard two-period general equilibrium model with uncertainty and incomplete asset markets. The notion of equilibrium examined is a fix-price one, which is an extension of an extant definition of fix-price equilibrium under certainty to the current framework, with endogenously determined rationing on net trades to attain market clearing. A point of interest - and an unexpected one - is that the possibility of arbitrage is not completely eliminated by the endogenous trading constraints, as shown by an example. Very weak assumptions are needed for the existence result, in particular, the asset return matrix need not have full column rank, allowing for redundant assets. The description of the model includes the consumption sets \(X^{i},\) utility functions \(u^{i},\) endowments \(e^{i}\) for each individual \(i\in I,\) and an asset return matrix \(R(p,q)\) that specifies the payoffs of assets in each state of nature \(s\) in \(\{1,\dots,S\},\) in units of account, at prices of commodities \(p\) and prices of assets \(q\). There are \(L+1\) commodities of which the last one, \(L+1,\) is the numeraire at each state \(s.\) There are \( A+1\) assets and asset number \(A+1\) is a numeraire asset which plays the role of the medium of exchange before the state of nature is known and after the state is known it is the numeraire commodity \((L+1,s)\) which performs this role. The following assumptions are made: {A1}. Each \(\;X^{i}= \mathbb{R}_{+}^{(L+1)S};\) {A2.} Each \(u^{i}\) is continuous, quasi-concave and weakly monotonically increasing in the numeraire commodity in every state of the world; {A3.} For each \(i,e^{i}\in X^{i}.\) Given a profile of prices \(\overline{p}\), for the commodities and \(\overline{ q}\), for the assets, a definition of equilibrium (with rationing), { at these prices}, is provided, the interest being in the specification of an allocation which is consistent with the prices \((\overline{p},\ove…
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91B50
zbMATH DE Number: 1839104
zbMATH Keywords: Incomplete asset market
zbMATH Keywords: Fix-price equilibrium
zbMATH Keywords: Arbitrage
author: P. Jean-Jacques Herings
author: Herakles M. Polemarchakis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1839104