Dynamically-Complete Markets Under Brownian Motion

25 Pages Posted: 3 Mar 2012 Last revised: 27 Aug 2019

See all articles by Theodoros Diasakos

Theodoros Diasakos

University of Stirling - Department of Economics

Date Written: June 11, 2019

Abstract

This paper investigates how continuous-time trading renders dynamically complete a financial market in which the underlying risk process is a Brownian motion. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, has been established in the literature for a single-commodity, pure-exchange economy with many heterogenous agents and where all intermediate flows of dividends, endowments, and utilities are analytic functions. In sharp contrast, the conditions given here suffice also for more general settings. The novelty of the present study lies in deriving analytical expressions for the dispersion coefficients of the securities' prices - by means of a mathematical approach that requires neither analyticity nor a particular economic environment. We assume only that pricing kernels and dividends satisfy standard growth and smoothness conditions (mild enough though to allow even for options). In this sense, our sufficient conditions for dynamic completeness apply irrespectively of preferences, endowments, and other structural elements (for instance, whether or not the budget constraints include only pure exchange).

Keywords: Dynamically-complete markets, Brownian motion, Asset pricing

JEL Classification: G10, G12

Suggested Citation

Diasakos, Theodoros, Dynamically-Complete Markets Under Brownian Motion (June 11, 2019). Available at SSRN: https://ssrn.com/abstract=2014765 or http://dx.doi.org/10.2139/ssrn.2014765

Theodoros Diasakos (Contact Author)

University of Stirling - Department of Economics ( email )

Stirling, FK9 4LA
United Kingdom

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