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

Author

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  • Ghislain Léveillé

    (Université Laval)

  • Emmanuel Hamel

    (Université Laval)

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.

Suggested Citation

  • Ghislain Léveillé & Emmanuel Hamel, 2018. "Conditional, Non-Homogeneous and Doubly Stochastic Compound Poisson Processes with Stochastic Discounted Claims," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 353-368, March.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:1:d:10.1007_s11009-017-9555-6
    DOI: 10.1007/s11009-017-9555-6
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    References listed on IDEAS

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    1. Leveille, Ghislain & Garrido, Jose, 2001. "Moments of compound renewal sums with discounted claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 217-231, April.
    2. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    3. Dassios, Angelos & Jang, Jiwook, 2008. "The distribution of the interval between events of a Cox process with shot noise intensity," LSE Research Online Documents on Economics 31864, London School of Economics and Political Science, LSE Library.
    4. Angelos Dassios & Jiwook Jang, 2008. "The Distribution of the Interval between Events of a Cox Process with Shot Noise Intensity," International Journal of Stochastic Analysis, Hindawi, vol. 2008, pages 1-14, November.
    5. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
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    Cited by:

    1. Franck Adékambi & Kokou Essiomle, 2021. "Asymptotic Tail Probability of the Discounted Aggregate Claims under Homogeneous, Non-Homogeneous and Mixed Poisson Risk Model," Risks, MDPI, vol. 9(7), pages 1-22, June.

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