Journal of Stochastic Analysis
Abstract
In this paper, we prove the Jacod-Yor Theorem for sigma martingales, a class of processes that generalize local martingales and play a pivotal role in financial mathematics. While the Jacod-Yor Theorem has been extensively studied for L2-martingales, martingales, and local martingales, no prior version exists for sigma martingales. Our result establishes the connection between sigma martingales and their martingale representation properties, addressing a critical gap in the literature. As an application, we prove the Second Fundamental Theorem of Asset Pricing for markets where price processes are modeled as sigma martingales.
Recommended Citation
Sohns, Moritz
(2025)
"THE JACOD-YOR THEOREM FOR SIGMA MARTINGALES AND THE SECOND FUNDAMENTAL,"
Journal of Stochastic Analysis: Vol. 6:
No.
2, Article 1.
DOI: 10.31390/josa.6.2.01
Available at:
https://repository.lsu.edu/josa/vol6/iss2/1
DOI
10.31390/josa.6.2.01