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Moments of renewal shot-noise processes and their applications

Jang, Jiwook, Dassios, Angelos ORCID: 0000-0002-3968-2366 and Zhao, Hongbiao (2018) Moments of renewal shot-noise processes and their applications. Scandinavian Actuarial Journal (8). pp. 727-752. ISSN 0346-1238

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Identification Number: 10.1080/03461238.2018.1452285


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.

Item Type: Article
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Additional Information: © 2018 Informa UK Limited, trading as Taylor & Francis Group
Divisions: Statistics
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
H Social Sciences > HG Finance
Q Science > QA Mathematics
Date Deposited: 11 Apr 2018 09:15
Last Modified: 15 May 2024 23:14

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