Moments of the Discounted Aggregate Claims with Delay Inter-Occurrence Distribution and Dependence Introduced by a FGM Copula

Franck Adekambi

A chapter in Probability, Combinatorics and Control from IntechOpen

Abstract: In this chapter, with renewal argument, we derive higher simple moments of the Discounted Compound Delay Renewal Risk Process (DCDRRP) when introducing dependence between the inter-occurrence time and the subsequent claim size. To illustrate our results, we assume that the inter-occurrence time is following a delay-Poisson process and the claim amounts is following a mixture of Exponential distribution, we then provide numerical results for the first two moments. The dependence structure between the inter-occurrence time and the subsequent claim size is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we obtain a general formula for all the moments of the DCDRRP process.

Keywords: compound delay-Poisson process; discounted aggregate claims; moments; FGM copula; constant interest rate (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:200892

DOI: 10.5772/intechopen.88699

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