Abstract We present a general equilibrium model with incomplete financial markets and numeraire assets.We assume that there are 2 periods of time, say today and tomorrow. In period 0, households exchange goods and assets and then consumption takes place; in period 1, one of S possible states of nature occurs. In each of them, assets pay their returns, which are measured in units of a given physical good, i.e., the numeraire commodity; households exchange goods; finally, consumption takes place.We define a consumption, portfolio holding, commodity and asset price vector as an equilibrium vector associated with a given economy, if at those prices and economies households maximize, and market clears. While the existence proof by Geneakoplos and Polemarchakis (Essays in honor of K.J. Arrow, vol 3, Cambridge University Press, Cambridge, pp 65–95, 1986) uses a fixed point argument, we provide an independent existence result in terms of variational inequalities. That approach allows us to get the desired existence result under some different and more general or realistic assumptions than those usually made in the literature.
Variational Formulation of a General Equilibrium Model with Incomplete Financial Markets and Numeraire Assets: Existence / Donato, Maria Bernadette*; Milasi, Monica; Villanacci, Antonio. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - STAMPA. - 179:(2018), pp. 425-451. [10.1007/s10957-018-1388-0]
Variational Formulation of a General Equilibrium Model with Incomplete Financial Markets and Numeraire Assets: Existence
DONATO, MARIA BERNADETTE
Membro del Collaboration Group
;Villanacci, AntonioMembro del Collaboration Group
2018
Abstract
Abstract We present a general equilibrium model with incomplete financial markets and numeraire assets.We assume that there are 2 periods of time, say today and tomorrow. In period 0, households exchange goods and assets and then consumption takes place; in period 1, one of S possible states of nature occurs. In each of them, assets pay their returns, which are measured in units of a given physical good, i.e., the numeraire commodity; households exchange goods; finally, consumption takes place.We define a consumption, portfolio holding, commodity and asset price vector as an equilibrium vector associated with a given economy, if at those prices and economies households maximize, and market clears. While the existence proof by Geneakoplos and Polemarchakis (Essays in honor of K.J. Arrow, vol 3, Cambridge University Press, Cambridge, pp 65–95, 1986) uses a fixed point argument, we provide an independent existence result in terms of variational inequalities. That approach allows us to get the desired existence result under some different and more general or realistic assumptions than those usually made in the literature.File | Dimensione | Formato | |
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