Author(s)

Winfrida Mwigilwa^1*, Jane Aduda², Bidima Martin Le Doux Mbele³, Ananda Kube⁴

¹Department of Mathematics, Pan African University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya.
²Department of Mathematics and Actuarial Sciences, Jomo Kenyatta, University of Agriculture and Technology, Nairobi, Kenya.
³Department of Mathematics, University of Yaounde I, Yaounde, Cameroon.
⁴Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya.

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.

Structure Condition (SC), Minimal Structure Condition (MSC), Natural Struc-ture Condition (NSC), Jacod Decomposition

Mwigilwa, W. , Aduda, J. , Le Doux Mbele, B. and Kube, A. (2022) Different Types of Structure Conditions of Semimartingale with Jacod Decomposition. Journal of Mathematical Finance, 12, 367-381. doi: 10.4236/jmf.2022.122021.