Appl Math Optim (2012) 65:293–314
Local Risk-Minimization for Defaultable Claims
with Recovery Process
Francesca Biagini · Alessandra Cretarola
Published online: 8 November 2011
© Springer Science+Business Media, LLC 2011
Abstract We study the local risk-minimization approach for defaultable claims with
random recovery at default time, seen as payment streams on the random interval
❏0,τ∧ T ❑, where T denotes the ﬁxed time-horizon. We ﬁnd the pseudo-locally risk-
minimizing strategy in the case when the agent information takes into account the
possibility of a default event (local risk-minimization with G-strategies) and we pro-
vide an application in the case of a corporate bond. We also discuss the problem of
ﬁnding a pseudo-locally risk-minimizing strategy if we suppose the agent obtains her
information only by observing the non-defaultable assets.
Keywords Defaultable markets · Local risk-minimization · Minimal martingale
measure · Pseudo-locally risk-minimizing strategy · Payment stream · Random
The aim of this paper is to discuss the problem of pricing and hedging defaultable
claims, i.e. options that can lose partially or totally their value if a default event oc-
curs, by means of local risk-minimization approach applied to payment streams.
Communicating Editor: Bernt Øksendal.
F. Biagini (
Department of Mathematics, LMU, Theresienstraße 39, 80333 Munich, Germany
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1,
06123 Perugia, Italy