Finance Stoch (2010) 14: 153–155 DOI 10.1007/s00780-009-0106-z
E R R AT U M
Valuation of default-sensitive claims under imperfect
information (Publisher’s Erratum)
Delia Coculescu· Hélyette Geman · Monique Jeanblanc
Published online: 28 August 2009 © Springer-Verlag 2009
Erratum to: Finance Stoch (2008) 12: 195–218
DOI10.1007/s00780-007-0060-6
Due to errors in the typesetting process, some parts of this article were rendered incorrectly in Finance and Stochastics 12(2): 195–218 (2008). The incorrect parts and their correct versions are given here.
(1) On page 199, the formula
dYt = μ (Yt, t ) dt+ σ (Yt, t ) dBt+ s (Yt, t ) dBt (2.1) = μ (Yt, t ) dt+ σ1(Yt, t ) dBt, (2.2)
The online version of the original article can be found under doi:10.1007/s00780-007-0060-6. D. Coculescu (
)Department of Mathematics, ETH, Rämistrasse 101, 8092 Zürich, Switzerland e-mail:[email protected]
H. Geman
Birkbeck University of London, Malet Street, London WC1E 7HX, UK e-mail:[email protected]
M. Jeanblanc
Equipe d’Analyse et Probabilités, Université d’Evry Val d’Essonne, rue du Père Jarlan, 91025 Evry Cedex, France
e-mail:[email protected] M. Jeanblanc
154 D. Coculescu et al.
should read
dYt = μ (Yt, t ) dt+ σ (Yt, t ) dBt+ s (Yt, t ) dBt (2.1) = μ (Yt, t ) dt+ σ1(Yt, t ) dβt, (2.2)
(2) On page 200, after Proposition 3.1, the passage
Proof If M is an (Ft)-local martingale, there exist an (Ft)-predictable process
and a constant m such that Mt = m + t
0hudBu. Since the process β is a (Gt)
-Brownian motion, M is a (Gt)-local martingale.
should read
Proof If M is an (Ft)-local martingale, there exist an (Ft)-predictable process
and a constant m such that Mt = m + t
0hudβu. Since the process β is a (Gt)
-Brownian motion, M is a (Gt)-local martingale.
(3) On page 200, the formula
Mt= t 0 σ1(Yu, u) σ (Yu, u)+ η (Yu, u) dBu, (3.4) Nt= t 0 σ1(Yu, u) σ (Yu, u)+ η (Yu, u) dDu. (3.5) should read Mt= t 0 σ1(Yu, u) σ (Yu, u)+ η (Yu, u) dβu, (3.4) Nt= t 0 σ1(Yu, u) σ (Yu, u)+ η (Yu, u) dDu. (3.5)
(4) On page 210, the passage
We choose a constant default barrier b∈ (0, x0)and suppose for the observa-tion process the form
dYt= rYtdt+ σ1YtdBt, Y0= x0, where σ1= √ σ2+ s2and βt=σ Bt+sB t σ1 . should read
We choose a constant default barrier b∈ (0, x0)and suppose for the observa-tion process the form
dYt= rYtdt+ σ1Ytdβt, Y0= x0, where σ1= √ σ2+ s2and β t=σ Bt+sB t σ1 .
Valuation of default-sensitive claims under imperfect information 155
(5) On page 214, the passage
We choose to define the observation process as
dYt= λ(θ − Yt)dt+ σ1dBt, Y0= x0,
with σ1= √
σ2+ s2 and β
t = (σ Bt + sBt)/σ1. The processes defined in
Re-mark 3.6 take here the particular forms
Mt= σ σ1 σ+ η t 0 eλudBu, Nt= σ η σ+ η t 0 eλudBu+ σ s σ+ η t 0 eλudBu with η= s2/σ. should read
We choose to define the observation process as
dYt= λ(θ − Yt)dt+ σ1dβt, Y0= x0,
with σ1= √
σ2+ s2 and β
t = (σ Bt + sBt)/σ1. The processes defined in
Re-mark 3.6 take here the particular forms
Mt= σ σ1 σ+ η t 0 eλudβu, Nt= σ η σ+ η t 0 eλudBu+ σ s σ+ η t 0 eλudBu with η= s2/σ.
(6) On page 216, the formula
dYt= μdt + σ1dBt,
should read
