Different Types of Structure Conditions of Semimartingale with Jacod Decomposition
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Date
2022
Authors
Mwigilwa, Winfrida
Aduda, Jane
Le Doux Mbele, Bidima Martin
Kube, Ananda
Journal Title
Journal ISSN
Volume Title
Publisher
Scientific Research Publishing Inc
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.
Description
research article
Keywords
Structure Condition (SC), Minimal Structure Condition (MSC), Natural Structure Condition (NSC), Jacod Decomposition
Citation
Mwigilwa, W., Aduda, J., Mbele, B.M.L.D. and Kube, A. (2022) Different Types of Structure Conditions of Semimartingale with Jacod Decomposition. Journal of Mathematical Finance , 12, 367-381. https://doi.org/10.4236/jmf.2022.122021