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

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

Abstract

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.

Keywords

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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