A simple characterization of dynamic completeness in continuous time

Theodoros Diasakos

    Research output: Working paper

    4 Downloads (Pure)

    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.).
    Original languageEnglish
    PublisherUniversity of St Andrews
    Number of pages47
    Publication statusPublished - Sept 2013

    Publication series

    NameSchool of Economics & Finance Discussion Paper 1312
    No.1312
    ISSN (Print)0962-4031
    ISSN (Electronic)2055-303X

    Keywords

    • Dynamically-complete markets
    • Geometric Brownian motion
    • Asset pricing

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