Constructing Random Times with Given Survival Processes and Applications to Valuation of Credit Derivatives

  • Pavel V. Gapeev
  • Monique Jeanblanc
  • Libo Li
  • Marek Rutkowski


We provide an explicit construction of a random time when the associated Azéma semimartingale (also known as the survival process) is given in advance. Our approach hinges on the use of a variant of Girsanov’s theorem combined with a judicious choice of the Radon-Nikodým density process. The proposed solution is also partially motivated by the classic example arising in the filtering theory.


Probability Measure Random Time Credit Default Swap Local Martingale Credit Derivative 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pavel V. Gapeev
    • 1
  • Monique Jeanblanc
    • 2
  • Libo Li
    • 3
  • Marek Rutkowski
    • 3
  1. 1.Department of MathematicsLondon School of EconomicsLondonUK
  2. 2.Département de MathématiquesUniversité d’Évry Val d’EssonneÉvry CedexFrance
  3. 3.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia

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