Valuation of default-sensitive claims under imperfect information (Publisher's Erratum)

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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:Delia.Coculescu@math.ethz.ch

H. Geman

Birkbeck University of London, Malet Street, London WC1E 7HX, UK e-mail:h.geman@bbk.ac.uk

M. Jeanblanc

Equipe d’Analyse et Probabilités, Université d’Evry Val d’Essonne, rue du Père Jarlan, 91025 Evry Cedex, France

e-mail:monique.jeanblanc@univ-evry.fr M. Jeanblanc

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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.

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_{+ s}2_{and β} t=σ Bt+sB t σ1 .

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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_{+ s}2 _{and β}

t = (σ Bt + sBt)/σ1. The processes defined in

Re-mark 3.6 take here the particular forms

M_t= σ σ1 σ+ η t 0 eλudBu, N_t= σ η σ+ η t 0 eλudBu+ σ s σ+ η t 0 eλudB_u 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_{+ s}2 _{and β}

t = (σ Bt + sBt)/σ1. The processes defined in

Re-mark 3.6 take here the particular forms

M_t= σ σ1 σ+ η t 0 eλudβu, N_t= σ η σ+ η t 0 eλudBu+ σ s σ+ η t 0 eλudB_u with η= s2/σ.

dYt= μdt + σ1dBt,

should read