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Conditional, Non-Homogeneous and Doubly Stochastic Compound Poisson Processes with Stochastic Discounted Claims

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Abstract

In this paper, we study the conditional, non-homogeneous and doubly stochastic compound Poisson process with stochastic discounted claims. We derive the moment generating functions of these risk processes and find their inverses, numerically or analytically, by using their corresponding characteristic functions. We then compare their distributions and some risk measures as the VaR and TVaR, and we examine the case where there is a possible dependence between the occurrence time and the severity of the claim.

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Authors and Affiliations

  1. École d’actuariat, Pavillon Paul Comtois, local 4157, 2425 rue de l’Agriculture, Université Laval, Québec, G1V 0A6, Canada

    Ghislain Léveillé & Emmanuel Hamel

Authors
  1. Ghislain Léveillé
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  2. Emmanuel Hamel
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Correspondence to Ghislain Léveillé.

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Léveillé, G., Hamel, E. Conditional, Non-Homogeneous and Doubly Stochastic Compound Poisson Processes with Stochastic Discounted Claims. Methodol Comput Appl Probab 20, 353–368 (2018). https://doi.org/10.1007/s11009-017-9555-6

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  • DOI: https://doi.org/10.1007/s11009-017-9555-6

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