In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Föllmer–Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Lévy process and the claims pay a predetermined...

Given a process with independent increments X (not necessarily a martingale) and a large class of square integrable r.v. H = f(X T ), f being the Fourier transform of a finite measure μ, we provide a direct expression for Kunita-Watanabe and Föllmer-Schweizer decompositions of H. The...