First passage time law for some Lévy processes with compound Poisson: Existence of a conditional density with incomplete observation

2014/02/09 by Waly Ngom, Ngom, Waly
Economics, Econometrics and Finance · Mathematics · #Banking stability, regulation, efficiency #Credit Risk and Financial Regulations #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1402.2000

18 pages

openalex publication_date 2014/02/09 · arxiv created 2014/11/22 · arxiv updated 2014/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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