Recursive moments of the aggregate discounted claims with Erlang inter-occurrence distribution and dependence introduced by a FGM Copula
Date
2019-08
Authors
Adekambi, Franck
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
In this paper, we investigate the computation of the moments of the discounted compound
renewal aggregate sums when introducing dependence between the inter-occurrence time and the
subsequent claim size. We first assume that the inter-occurrence time is following an Erlang
distribution and later extend our result to a mixture of Erlangs distribution. The dependence
structure between the interoccurrence 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 any mth order moment. The results are illustrated with applications to
premium calculation, moment matching methods, as well as inflation stress scenarios in Solvency
Il.
Description
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya
Keywords
Compound renewal process, Discounted aggregate claims, Moments, FGM copula, Mix Erlang distribution