Itô formula for stochastic integrals w.r.t. compensated Poisson random measures on separable Banach spaces

Option Pricing in Hilbert Space-Valued Jump-Diffusion Models Using Partial Integro-Differential Equations

“…3.11]. The prerequisite for this theorem is a strong integrability condition, which is satisfied due to [29,Thm. 3.12], since…”

“…4.12]. In order to show that the integral with respect to the compensated Poisson measure is a martingale too, we apply [29,Thm. 3.11].…”

Itô’s Formula for Banach-space-valued Jump Processes Driven by Poisson Random Measures

“…However, this is necessary in case the formula is used to find the generator of a Markov process. In this article, we provide an improvement of the work of [14]. Even if the methods are similar, the current article is presented in a clearer and direct way, due to integrands having general integrability conditions.…”

“…In this context, Itô's formula was originally given in [14]. However, there it was only proven for a smaller class of integrands, as stochastic integration for Banach space valued integrands was still not understood in the generality of the forthcoming papers [9], [10].…”

“…Even if the methods are similar, the current article is presented in a clearer and direct way, due to integrands having general integrability conditions. The mark space (E, E), associated to the compensated Poisson random measure, is also allowed to be more general than in [14], where E has been a separable Banach space. We refer Remark 2.1 and Remark 3.2, where this generalization is discussed.…”