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A Simple Characterization of Dynamic Completeness in Continuous Time

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  • Diasakos, Theodoros M

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.)

Suggested Citation

  • Diasakos, Theodoros M, 2013. "A Simple Characterization of Dynamic Completeness in Continuous Time," SIRE Discussion Papers 2013-91, Scottish Institute for Research in Economics (SIRE).
    • Handle: RePEc:edn:sirdps:508
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    More about this item

    Keywords

    Dynamically-Complete Markets; Geometric Brownian Motion; Asset Pricing;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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