Martingale densities for general asset prices

Abstract

This paper discusses some properties of general asset prices in continuous time. We introduce the concept of a martingale density which is a generalization of an equivalent martingale measure, and we show that absence of arbitrage plus some technical conditions implies the existence of a martingale density. This is in turn already sufficient to derive a recent result of Back (1991) on local risk premia for asset returns. As an application, we obtain a simple condition, valid in arbitrary information structures, for the drift part of discounted security gains to be absolutely continuous with respect to the variance process of the martingale part. © 1992.