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

Fouad Marri; Franck Adékambi; Khouzeima Moutanabbir

doi:10.3390/risks6030086

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

Fouad Marri, Franck Adékambi, Khouzeima Moutanabbir

School of Economics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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.

Original language	English
Article number	86
Journal	Risks
Volume	6
Issue number	3
DOIs	https://doi.org/10.3390/risks6030086
Publication status	Published - Sept 2018

Keywords

Archimedean copulas
Copulas
Discounted aggregate claims
Renewal process

ASJC Scopus subject areas

Accounting
Economics, Econometrics and Finance (miscellaneous)
Strategy and Management

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10.3390/risks6030086

Cite this

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abstract = "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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AU - Adékambi, Franck

AU - Moutanabbir, Khouzeima

PY - 2018/9

Y1 - 2018/9

N2 - 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.

AB - 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.

KW - Archimedean copulas

KW - Copulas

KW - Discounted aggregate claims

KW - Renewal process

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VL - 6

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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