TITLE:
Different Types of Structure Conditions of Semimartingale with Jacod Decomposition
AUTHORS:
Winfrida Mwigilwa, Jane Aduda, Bidima Martin Le Doux Mbele, Ananda Kube
KEYWORDS:
Structure Condition (SC), Minimal Structure Condition (MSC), Natural Struc-ture Condition (NSC), Jacod Decomposition
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.12 No.2,
May
26,
2022
ABSTRACT: The objective of this article is to use Jacod decomposition to develop different types of semimartingale structure conditions. We make the following contributions to that end: When a continuous semimartingale meets the structure condition (SC), we prove that there is a minimal martingale density and a predictable variation part. When a special semimartingale meets the minimal structure condition (MSC) and the natural structure condition (NSC), we derive a Radon-Nikodym decomposition and a Natural Kunita-Watanabe decomposition from a given sigma martingale density, which is written under the Jacod decomposition.