Moments of renewal shot-noise processes and their applications

Jiwook Jang, Angelos Dassios and Hongbiao Zhao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: renewal shot-noise processes; discounted aggregate claims; actuarial net premium; piecewise-deterministic Markov processes; martingale method; Monte Carlo exact simulation; credit risk; reliability (search for similar items in EconPapers)
JEL-codes: F3 G3 G32 (search for similar items in EconPapers)
Date: 2018
New Economics Papers: this item is included in nep-cmp and nep-ore
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Citations: View citations in EconPapers (5)

Published in Scandinavian Actuarial Journal, 2018(8), pp. 727-752. ISSN: 0346-1238

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:87428

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