Default times, no-arbitrage conditions and changes of probability measures

In this paper, we give a financial justification, based on no-arbitrage conditions, of the (H)-hypothesis in default time modeling. We also show how the (H)-hypothesis is affected by an equivalent change of probability measure. The main technique used here is the theory of progressive enlargements of filtrations.

[1]  Monique Jeanblanc,et al.  PARTIAL INFORMATION AND HAZARD PROCESS , 2005 .

[2]  Shigeo Kusuoka,et al.  A Remark on default risk models , 1999 .

[3]  Kiyosi Itô,et al.  Transformation of Markov processes by multiplicative functionals , 1965 .

[4]  P. Meyer,et al.  Probabilités et potentiel , 1966 .

[5]  R. Frey,et al.  PRICING CORPORATE SECURITIES UNDER NOISY ASSET INFORMATION , 2009 .

[6]  Séminaire de Probabilités XII , 1978 .

[7]  Xin Guo,et al.  Credit Risk Models with Incomplete Information , 2009, Math. Oper. Res..

[8]  Martin T. Barlow,et al.  Study of a filtration expanded to include an honest time , 1978 .

[9]  K. Giesecke,et al.  Forecasting Default in the Face of Uncertainty , 2004 .

[10]  F. Delbaen,et al.  A general version of the fundamental theorem of asset pricing , 1994 .

[11]  J. Azéma Quelques applications de la théorie générale des processus. I , 1972 .

[12]  Delia Coculescu,et al.  Valuation of default-sensitive claims under imperfect information , 2008, Finance Stochastics.

[13]  A. Nikeghbali,et al.  HAZARD PROCESSES AND MARTINGALE HAZARD PROCESSES , 2008, 0807.4958.

[14]  M. Yor,et al.  Grossissements de filtrations: exemples et applications , 1985 .

[15]  T. Jeulin Grossissement d'une filtration et applications , 1979 .

[16]  A. Nikeghbali An essay on the general theory of stochastic processes , 2005, math/0506581.

[17]  Peter Imkeller,et al.  Random times at which insiders can have free lunches , 2002 .

[18]  M. Yor,et al.  Grossissement d’une filtration et semi-martingales : Formules explicites , 1978 .

[19]  Roger Mansuy,et al.  Random Times and Enlargements of Filtrations in a Brownian Setting , 2006 .

[20]  Monique Jeanblanc,et al.  Hazard rate for credit risk and hedging defaultable contingent claims , 2004, Finance Stochastics.

[21]  Robert J. Elliott,et al.  On Models of Default Risk , 2000 .

[22]  Thierry Jeulin,et al.  Nouveaux résultats sur le grossissement des tribus , 1978 .

[23]  Marc Yor,et al.  A definition and some characteristic properties of pseudo-stopping times , 2004, math/0406459.

[24]  M. Émery,et al.  On certain probabilities equivalent to Coin-Tossing, d'Après Schachermayer , 1999 .

[25]  T. Cotton ‘FLIPPING THE COIN’: MODELS FOR SOCIAL JUSTICE AND THE MATHEMATICS CLASSROOM , 1999 .

[26]  Marc Yor,et al.  Changes of filtrations and of probability measures , 1978 .

[27]  Monique Jeanblanc,et al.  What happens after a default: The conditional density approach , 2009, 0905.0559.

[28]  A. Nikeghbali Non-stopping times and stopping theorems , 2005, math/0505316.

[29]  C. Dellacherie Capacités et processus stochastiques , 1972 .

[30]  T. Jeulin Semi-Martingales et Grossissement d’une Filtration , 1980 .

[31]  D. Duffie,et al.  Term Structures of Credit Spreads with Incomplete Accounting Information , 2001, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[32]  P. Protter Stochastic integration and differential equations , 1990 .