Neumann series on the recursive moments of copula-dependent aggregate discounted claims

Siti Norafidah Mohd Ramli, Jiwook Jang

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
30 Downloads (Pure)


We study the recursive moments of aggregate discounted claims, where the dependence between the inter-claim time and the subsequent claim size is considered. Using the general expression for the m-th order moment proposed by Léveillé and Garrido (Scand. Actuar. J. 2001, 2, 98–110), which takes the form of the Volterra integral equation (VIE), we used the method of successive approximation to derive the Neumann series of the recursive moments. We then compute the first two moments of aggregate discounted claims, i.e., its mean and variance, based on the Neumann series expression, where the dependence structure is captured by a Farlie–Gumbel–Morgenstern (FGM) copula, a Gaussian copula and a Gumbel copula with exponential marginal distributions. Insurance premium calculations with their figures are also illustrated.
Original languageEnglish
Pages (from-to)195-210
Number of pages16
Issue number2
Publication statusPublished - Jun 2014

Bibliographical note

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  • aggregate discounted claims
  • moments
  • copulas
  • Volterra integral equation
  • Neumann series
  • insurance premium


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