The strong predictable representation property in initially enlarged filtrations under the density hypothesis

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Fontana, Claudio¹ 

[1] Paris Diderot Univ, Lab Probabil & Modeles Aleatoires, Paris, France

关键词: Initial enlargement of filtration;    Density hypothesis;    Martingale representation property;    Hedging;    Insider information;   

DOI  :  10.1016/j.spa.2017.06.015

来源: Elsevier

【 摘 要 】

We study the strong predictable representation property in filtrations initially enlarged with a random variable L. We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the existing martingale representation results and does not rely on the equivalence between the conditional and the unconditional laws of L. Depending on the behavior of the density process at zero, different forms of martingale representation are established. The results are illustrated in the context of hedging contingent claims under insider information. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free