演講訊息 TALKS

Abstract Being inspired by the work of Imkeller et al. (2001), which first develops a measured-valued version of Malliavin calculus to study the enlargement of filtration by an “exogenous” random variable on the Wiener space, in this article, we consider the enlargement of filtration on the Poisson space. We construct a measure-valued Malliavin calculus on the Poisson space with the Malliavin type calculus defined in Mensi and Privault (2003). Without resorting to the traditional Jacod’s condition (Jacod (1985)) nor its local version (Jeanblanc and Song (2012)), the measure-valued Poisson Malliavin calculus can be applied to compute the “information drift”, which follows the similar spirit in Imkeller et al. (2001). However, in contrast to the latter work, our result can be applied for a general L^2 -integrable “exogenous” random variable, while that in Imkeller et al. (2001) requires more restrictive Malliavin differentiability. Finally, we illustrate a concrete application of our theory for an example extracted from Mensi and Privault (2003).