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Risks 2018, 6(3), 86;

Moments of Compound Renewal Sums with Dependent Risks Using Mixing Exponential Models

Department of Statistics and Actuarial Science, Institut National de Statistique et d’Economie Appliquée, INSEA, Rabat 10112, Morocco
School of Economics, University of Johannesburg, Johannesburg 2006, South Africa
Department of Mathematics and Actuarial Science, The American University in Cairo, New Cairo 11835, Egypt
Author to whom correspondence should be addressed.
Received: 20 July 2018 / Revised: 20 August 2018 / Accepted: 22 August 2018 / Published: 24 August 2018
(This article belongs to the Special Issue Risk, Ruin and Survival: Decision Making in Insurance and Finance)
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In this paper, we study the discounted renewal aggregate claims with a full dependence structure. Based on a mixing exponential model, the dependence among the inter-claim times, the claim sizes, as well as the dependence between the inter-claim times and the claim sizes are included. The main contribution of this paper is the derivation of the closed-form expressions for the higher moments of the discounted aggregate renewal claims. Then, explicit expressions of these moments are provided for specific copulas families and some numerical illustrations are given to analyze the impact of dependency on the moments of the discounted aggregate amount of claims. View Full-Text
Keywords: renewal process; discounted aggregate claims; copulas; archimedean copulas renewal process; discounted aggregate claims; copulas; archimedean copulas
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Marri, F.; Adékambi, F.; Moutanabbir, K. Moments of Compound Renewal Sums with Dependent Risks Using Mixing Exponential Models. Risks 2018, 6, 86.

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