Martingale densities for general asset prices. (English) Zbl 0762.90014

Summary: 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 K. Back [ibid. 20, No. 4, 371-395 (1991; Zbl 0727.90014)] 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.


91B62 Economic growth models


Zbl 0727.90014
Full Text: DOI


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