It^os formula for finite variation Levy processes: The case of non-smooth functions

Extending It^os formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-It^o, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of It^os formula for diffusion processes where the Meyer-It^o assumptions are weakened even further. We study a version of It^os formula for multi-dimensional finite variation Levy processes assuming that the underlying function is continuous and admits weak derivatives. We also discuss some applications of this extension, particularly in finance.

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 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.