First passage time law for some Lévy processes with compound Poisson: Existence of a conditional density with incomplete observation
Abstract
We study the default risk in incomplete information. That means, we model the value of a firm by one Lévy process which is the sum of brownian motion with drift and compound Poisson process. This Lévy process can not be observed completely and we let an other process which representes the available information on the firm. We obtain an equation safisfied by the conditional density of the default time given the available information and closed form expression for the density.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.2000
 Bibcode:
 2014arXiv1402.2000N
 Keywords:

 Mathematics  Probability
 EPrint:
 18 pages