Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/103600
Authors: 
Ramli, Siti Norafidah Mohd
Jang, Jiwook
Year of Publication: 
2014
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Publisher:] MDPI [Place:] Basel [Volume:] 2 [Year:] 2014 [Issue:] 2 [Pages:] 195-210
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.
Subjects: 
aggregate discounted claims
moments
copulas
Volterra integral equation
Neumann series
insurance premium
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/3.0/
Document Type: 
Article
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