Title

Moments of compound renewal sums with dependent risks using mixing exponential models

Author's Department

Mathematics & Actuarial Science Department

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https://doi.org/10.3390/risks6030086

Document Type

Research Article

Publication Title

Risks

Publication Date

9-1-2018

doi

10.3390/risks6030086

Abstract

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. 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.

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