Neumann Series on the Recursive Moments of Copula-Dependent Aggregate Discounted Claims

Risks

Siti Norafidah Mohd Ramli¹ 

关键词: aggregate discounted claims;    moments;    copulas;    Volterra integral equation;    Neumann series;    insurance premium;   

DOI  :  10.3390/risks2020195

来源: mdpi

【 摘 要 】

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 theorder 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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.