Moments of renewal shot-noise processes and their applications

Jiwook Jang, Angelos Dassios, Hongbiao Zhao

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)727-752
Number of pages26
JournalScandinavian Actuarial Journal
Volume2018
Issue number8
Early online date20 Mar 2018
DOIs
Publication statusPublished - 14 Sep 2018

Keywords

  • Renewal shot-noise processes
  • discounted aggregate claims
  • actuarial net premium
  • piecewise-deterministic Markov processes
  • martingale method
  • Monte Carlo exact simulation
  • credit risk
  • reliability

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