The Föllmer–Schweizer decomposition: Comparison and description

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.