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2019 Closed-form formulas for the distribution of the jumps of doubly-stochastic Poisson processes
Arturo Valdivia
Electron. Commun. Probab. 24: 1-12 (2019). DOI: 10.1214/19-ECP221

Abstract

We study the obtainment of closed-form formulas for the distribution of the jumps of a doubly-stochastic Poisson process. The problem is approached in two ways. On the one hand, we translate the problem to the computation of multiple derivatives of the Hazard process cumulant generating function; this leads to a closed-form formula written in terms of Bell polynomials. On the other hand, for Hazard processes driven by Lévy processes, we use Malliavin calculus in order to express the aforementioned distributions in an appealing recursive manner. We outline the potential application of these results in credit risk.

Citation

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Arturo Valdivia. "Closed-form formulas for the distribution of the jumps of doubly-stochastic Poisson processes." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP221

Information

Received: 2 January 2017; Accepted: 22 February 2019; Published: 2019
First available in Project Euclid: 21 March 2019

zbMATH: 1412.60060
MathSciNet: MR3933037
Digital Object Identifier: 10.1214/19-ECP221

Subjects:
Primary: 60G22, 60G51, 60H07, 91G40

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