A simple characterization of dynamic completeness in continuous time
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.).
Citation
Diasakos , T 2013 ' A simple characterization of dynamic completeness in continuous time ' School of Economics & Finance Discussion Paper 1312 , no. 1312 , University of St Andrews .
ISSN
0962-4031Type
Working or discussion paper
Rights
(c) 2013 the author
Description
Under review (second round) by Mathematical Finance (Online ISSN: 1467-9965)Collections
URL
http://ideas.repec.org/p/san/wpecon/1312.htmlhttp://www.st-andrews.ac.uk/economics/repecfiles/4/1312.pdf
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2014765
http://carloalberto.it/assets/working-papers/no.211.pdf
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