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A Simple Characterization of Dynamic Completeness in Continuous Time

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  • Theodoros M. Diasakos

    ()
    (University of St Andrews)

Abstract

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities' dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.).

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Bibliographic Info

Paper provided by Department of Economics, University of St. Andrews in its series Discussion Paper Series, Department of Economics with number 201312.

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Date of creation: 20 May 2012
Date of revision: 02 Sep 2013
Handle: RePEc:san:wpecon:1312

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Keywords: Dynamically-Complete Markets; Geometric Brownian Motion; Asset Pricing;

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