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Different Types of Structure Conditions of Semimartingale with Jacod Decomposition

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

Journal of Mathematical Finance·Volume 12 (2022)·Pages 367–381·Published 11 May 2022·DOI10.4236/jmf.2022.122021

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.

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

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Different Types of Structure Conditions of Semimartingale with Jacod Decomposition

Abstract

References (22)