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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.

MSC:

91B62 Economic growth models

Citations:

Zbl 0727.90014
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