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.
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This paper is dedicated to Professor Eckhard Platen on the occasion of his 60th birthday. Even though the topic of this work is not related to his exciting benchmark approach, we hope he will find some interest in this research.
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Gapeev, P.V., Jeanblanc, M., Li, L., Rutkowski, M. (2010). Constructing Random Times with Given Survival Processes and Applications to Valuation of Credit Derivatives. In: Chiarella, C., Novikov, A. (eds) Contemporary Quantitative Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03479-4_14
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DOI: https://doi.org/10.1007/978-3-642-03479-4_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03478-7
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