  In the context of a locally risk-minimizing approach, the problem of hedging
defaultable claims and their Follmer-Schweizer decompositions are discussed in
a structural model. This is done when the underlying process is a finite
variation Levy process and the claims pay a predetermined payout at maturity,
contingent on no prior default. More precisely, in this particular framework,
the locally risk-minimizing 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.
