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Sarmanov Family of Bivariate Distributions for Multivariate Loss Reserving Analysis

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  • Anas Abdallah
  • Jean-Philippe Boucher
  • Hélène Cossette
  • Julien Trufin

Abstract

The correlation among multiple lines of business plays a critical role in aggregating claims and thus determining loss reserves for an insurance portfolio. We show that the Sarmanov family of bivariate distributions is a convenient choice to capture the dependencies introduced by various sources, including the common calendar year, accident year, and development period effects. The density of the bivariate Sarmanov distributions with different marginals can be expressed as a linear combination of products of independent marginal densities. This pseudo-conjugate property greatly reduces the complexity of posterior computations. In a case study, we analyze an insurance portfolio of personal and commercial auto lines from a major U.S. property-casualty insurer.

Suggested Citation

  • Anas Abdallah & Jean-Philippe Boucher & Hélène Cossette & Julien Trufin, 2016. "Sarmanov Family of Bivariate Distributions for Multivariate Loss Reserving Analysis," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(2), pages 184-200, April.
    • Handle: RePEc:taf:uaajxx:v:20:y:2016:i:2:p:184-200
    DOI: 10.1080/10920277.2016.1161525
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    Citations

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    Cited by:

    1. Catalina Bolancé & Raluca Vernic, 2020. "Frequency and Severity Dependence in the Collective Risk Model: An Approach Based on Sarmanov Distribution," Mathematics, MDPI, vol. 8(9), pages 1-17, August.
    2. Denuit, Michel & Lu, Yang, 2020. "Wishart-Gamma mixtures for multiperil experience ratemaking, frequency-severity experience rating and micro-loss reserving," LIDAM Discussion Papers ISBA 2020016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Anas Abdallah & Lan Wang, 2023. "Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves," Risks, MDPI, vol. 11(11), pages 1-37, October.
    4. Tzougas, George & Pignatelli di Cerchiara, Alice, 2021. "The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 602-625.
    5. Ratovomirija, Gildas & Tamraz, Maissa & Vernic, Raluca, 2017. "On some multivariate Sarmanov mixed Erlang reinsurance risks: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 197-209.
    6. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.
    7. Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2023. "EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects," LSE Research Online Documents on Economics 118826, London School of Economics and Political Science, LSE Library.

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