Hedging of defaultable claims in a structural model using a locally risk-minimizing approach

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 payout at maturity, contingent on no prior default. More precisely, in this particular framework, the locally riskminimizing approach is carried out when the underlying process has jumps, the derivative is linked to a default event, and the probability measure is not necessarily risk-neutral.