This paper proposes two main contributions concerning the Föllmer-Schweizer decomposition (called hereafter the FS-decomposition). First we completely elaborate the relationship between this decomposition and the Galtchouk-Kunita-Watanabe decomposition under the minimal martingale measure. The difference between these two decompositions is highlighted in a very practical example, and the martingale tools that enhance this difference are illustrated in the semimartingale framework as well. The second main contribution focuses on the description of the FS-decomposition using the predictable characteristics. © 2010 Elsevier B.V. All rights reserved.
Choulli, T., Vandaele, N., & Vanmaele, M. (2010). The Föllmer-Schweizer decomposition: Comparison and description. Stochastic Processes and Their Applications, 120(6), 853–872. https://doi.org/10.1016/j.spa.2010.02.004