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Moments of renewal shot-noise processes and their applications

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  • Jiwook Jang
  • Angelos Dassios
  • Hongbiao Zhao

Abstract

In this paper, we study the family of renewal shot-noise processes. The Feynmann–Kac formula is obtained based on the piecewise deterministic Markov process theory and the martingale methodology. We then derive the Laplace transforms of the conditional moments and asymptotic moments of the processes. In general, by inverting the Laplace transforms, the asymptotic moments and the first conditional moments can be derived explicitly; however, other conditional moments may need to be estimated numerically. As an example, we develop a very efficient and general algorithm of Monte Carlo exact simulation for estimating the second conditional moments. The results can be then easily transformed to the counterparts of discounted aggregate claims for insurance applications, and we apply the first two conditional moments for the actuarial net premium calculation. Similarly, they can also be applied to credit risk and reliability modelling. Numerical examples with four distribution choices for interarrival times are provided to illustrate how the models can be implemented.

Suggested Citation

  • Jiwook Jang & Angelos Dassios & Hongbiao Zhao, 2018. "Moments of renewal shot-noise processes and their applications," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(8), pages 727-752, September.
    • Handle: RePEc:taf:sactxx:v:2018:y:2018:i:8:p:727-752
    DOI: 10.1080/03461238.2018.1452285
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    Cited by:

    1. Lautier, Jackson P. & Pozdnyakov, Vladimir & Yan, Jun, 2023. "Pricing time-to-event contingent cash flows: A discrete-time survival analysis approach," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 53-71.

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