On the weak representation property in progressively enlarged filtrations with an application in exponential utility maximization

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Di Tella, Paolo¹ 

[1] Tech Univ Dresden, Inst Math Stochast, Zellescher Weg 12-14, D-01069 Dresden, Germany

关键词: Weak representation property;    Semimartingales;    Progressive enlargement of filtrations;    Exponential utility maximization;   

DOI  :  10.1016/j.spa.2019.03.013

来源: Elsevier

【 摘 要 】

In this paper we show that the weak representation property of a semimartingale X with respect to a filtration IF is preserved in the progressive enlargement G by a random time tau avoiding F-stopping times and such that F is immersed in G. As an application of this, we can solve an exponential utility maximization problem in the enlarged filtration G following the dynamical approach, based on suitable BSDEs, both over the fixed-time horizon [0, T], T > 0, and over the random -time horizon [0, T Lambda tau]. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free