Conditional Law of the Hitting Time for a Lévy Process in Incomplete Observation

Waly  Ngom

doi:10.4236/jmf.2015.55041

Waly Ngom^1,2

Abstract: We study the default risk in incomplete information. That means we model the value of a firm by a Lévy process which is the sum of a Brownian motion with drift and a compound Poisson process. This Lévy process cannot be completely observed, and another process represents the available information on the firm. We obtain a stochastic Volterra equation satisfied by the conditional density of the default time given the available information. The uniqueness of solution of this equation is proved. Numerical examples of (conditional) density are also given.

Keywords: Conditional Density, Default Time, Lévy Processes, Filtering Theory, Stochastic Voltera Equations

Cite this paper: Ngom, W. (2015) Conditional Law of the Hitting Time for a Lévy Process in Incomplete Observation. Journal of Mathematical Finance, 5, 505-524. doi: 10.4236/jmf.2015.55041.

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