Endogenous Completeness of Diffusion Driven Equilibrium Markets

77 Pages Posted: 28 Sep 2009

See all articles by Julien Hugonnier

Julien Hugonnier

Centre for Economic Policy Research (CEPR); École Polytechnique Fédérale de Lausanne

Semyon Malamud

Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Eugene Trubowitz

Swiss Federal Institute of Technology Zurich

Abstract

We study the existence of equilibria with endogenously complete markets in a continuous-time, heterogenous agents economy driven by a multidimensional diffusion process. Our main results show that if prices are real analytic as functions of time and the state variables of the model then a sufficient condition for market completeness is that the volatility of dividends be nondegenerate. In contrast to previous research, our formulation does not require that securities pay terminal dividends and thus allows for both finite or infinite horizon economies. We illustrate our results by providing easily applicable conditions for market completeness in two benchmark cases: that where the state variables are given by a vector autoregressive process and that where they are given by a vector of autonomous diffusion processes. We also provide counterexamples which show that real analyticity cannot be dispensed with if one is to deduce dynamic market completeness from the structure of dividends.

Keywords: continuous-time finance, dynamic market completeness, general equilibrium theory

JEL Classification: D51, D52, D53, G11, G12

Suggested Citation

Hugonnier, Julien and Malamud, Semyon and Trubowitz, Eugene, Endogenous Completeness of Diffusion Driven Equilibrium Markets. Swiss Finance Institute Research Paper No. 09-41, Available at SSRN: https://ssrn.com/abstract=1479502 or http://dx.doi.org/10.2139/ssrn.1479502

Julien Hugonnier

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

École Polytechnique Fédérale de Lausanne ( email )

Quartier UNIL Dorigny
Extranef
Lausanne, CH-1015
Switzerland

HOME PAGE: http://https://www.epfl.ch/labs/sfi-jh/

Semyon Malamud (Contact Author)

Ecole Polytechnique Federale de Lausanne ( email )

Lausanne, 1015
Switzerland

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Eugene Trubowitz

Swiss Federal Institute of Technology Zurich ( email )

Lausanne CH-1001
Switzerland

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