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

Siti Norafidah Mohd Ramli, Jiwook Jang

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Abstract

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
JournalRisks
Volume2
Issue number2
DOIs
Publication statusPublished - Jun 2014

Bibliographical note

Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please check publisher website http://www.mdpi.com/home.

Keywords

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

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