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Nonparametric estimation of the claim amount in the strong stability analysis of the classical risk model

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  • Touazi, A.
  • Benouaret, Z.
  • Aissani, D.
  • Adjabi, S.

Abstract

This paper presents an extension of the strong stability analysis in risk models using nonparametric kernel density estimation for the claim amounts. First, we detail the application of the strong stability method in risk models realized by V. Kalashnikov in 2000. In particular, we investigate the conditions and the approximation error of the real model, in which the probability distribution of the claim amounts is not known, by the classical risk model with exponentially distributed claim sizes. Using the nonparametric approach, we propose different kernel estimators for the density of claim amounts in the real model. A simulation study is performed to numerically compare between the approximation errors (stability bounds) obtained using the different proposed kernel densities.

Suggested Citation

  • Touazi, A. & Benouaret, Z. & Aissani, D. & Adjabi, S., 2017. "Nonparametric estimation of the claim amount in the strong stability analysis of the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 78-83.
    • Handle: RePEc:eee:insuma:v:74:y:2017:i:c:p:78-83
    DOI: 10.1016/j.insmatheco.2017.02.007
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    References listed on IDEAS

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    1. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2008. "Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 746-762, April.
    2. Malec, Peter & Schienle, Melanie, 2014. "Nonparametric kernel density estimation near the boundary," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 57-76.
    3. Bernd Heidergott & Arie Hordijk & Nicole Leder, 2010. "Series Expansions for Continuous-Time Markov Processes," Operations Research, INFORMS, vol. 58(3), pages 756-767, June.
    4. Marceau, Etienne & Rioux, Jacques, 2001. "On robustness in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 167-185, October.
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    Cited by:

    1. Jorge Wilson Euphasio Junior & João Vinícius França Carvalho, 2022. "Resseguro e Capital de Solvência: Atenuantes da Probabilidade de Ruína de SeguradorasReinsurance and Solvency Capital: Mitigating Insurance Companies’ Ruin Probability," RAC - Revista de Administração Contemporânea (Journal of Contemporary Administration), ANPAD - Associação Nacional de Pós-Graduação e Pesquisa em Administração, vol. 26(1), pages 200191-2001.
    2. Aicha Bareche & Mouloud Cherfaoui, 2019. "Sensitivity of the Stability Bound for Ruin Probabilities to Claim Distributions," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1259-1281, December.

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