Change of measure up to a random time: Details

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Kreher, Doerte¹ 

[1] Humboldt Univ, Berlin, Germany

关键词: Random times;    Change of measure;    Progressive enlargement of filtrations;    NFLVR;   

DOI  :  10.1016/j.spa.2016.09.001

来源: Elsevier

【 摘 要 】

This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probability measure up to and after an honest time, and changes of probability measure up to a pseudo-stopping time. Moreover, we apply our results to construct a change of probability measure that is equivalent to the enlargement formula and to build, for a certain class of pseudo-stopping times, a class of measure changes that preserve the pseudo-stopping time property. Furthermore,. we study for a price process modeled by a continuous semimartingale the stability of the No Free Lunch with Vanishing Risk (NFLVR) property up to a random time, that avoids stopping times, in the progressively enlarged filtration and provide sufficient conditions for this stability in terms of the Azema supermartingale. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free