A Simple Characterization of Dynamic Completeness in Continuous Time

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.)

Comparative Statics of Asset Prices: the effect of other assets' risk

Currently, financial economics is unable to predict changes in asset prices with respect to changes in the underlying risk factors, even when an asset's dividend is independent of a given factor. This paper takes steps towards addressing this issue by highlighting a crucial component of wealth effects on asset prices hitherto ignored by the literature. Changes in wealth do not only alter an agents risk aversion, but also her perceived 'riskiness' of a security. The latter enhances significantly the extent to which market- clearing leads to endogenously-generated correlation across asset prices, over and above that induced by correlation between payoffs, giving the appearance of 'contagion.'