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Abstract: We present a general model for default time, making precise the role of theintensity process, and showing that this process allows for a knowledge of theconditional distribution of the default only -before the default-. This lack ofinformation is crucial while working in a multi-default setting. In a singledefault case, the knowledge of the intensity process does not allow to computethe price of defaultable claims, except in the case where immersion property issatisfied. We propose in this paper the density approach for default time. Thedensity process will give a full characterization of the links between thedefault time and the reference filtration, in particular -after the defaulttime-. We also investigate the description of martingales in the fullfiltration in terms of martingales in the reference filtration, and the impactof Girsanov transformation on the density and intensity processes, and also onthe immersion property.



Autor: Nicole El Karoui PMA, CMAP, Monique Jeanblanc DP, Ying Jiao PMA

Fuente: https://arxiv.org/







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