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On Sarmanov Mixed Erlang Risks In Insurance Applications

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  • Hashorva, Enkelejd
  • Ratovomirija, Gildas

Abstract

In this paper we consider an extension to the aggregation of the FGM mixed Erlang risks, proposed by Cossette et al. (2013 Insurance: Mathematics and Economics, 52, 560–572), in which we introduce the Sarmanov distribution to model the dependence structure. For our framework, we demonstrate that the aggregated risk belongs to the class of Erlang mixtures. Following results from S. C. K. Lee and X. S. Lin (2010 North American Actuarial Journal, 14(1) 107–130), G. E. Willmot and X. S. Lin (2011 Applied Stochastic Models in Business and Industry, 27(1) 8–22), analytical expressions of the contribution of each individual risk to the economic capital for the entire portfolio are derived under both the TVaR and the covariance capital allocation principle. By analysing the commonly used dependence measures, we also show that the dependence structure is wide and flexible. Numerical examples and simulation studies illustrate the tractability of our approach.

Suggested Citation

  • Hashorva, Enkelejd & Ratovomirija, Gildas, 2015. "On Sarmanov Mixed Erlang Risks In Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 45(1), pages 175-205, January.
    • Handle: RePEc:cup:astinb:v:45:y:2015:i:01:p:175-205_00
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    Citations

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    Cited by:

    1. Ignatieva, Katja & Landsman, Zinoviy, 2019. "Conditional tail risk measures for the skewed generalised hyperbolic family," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 98-114.
    2. Gildas Ratovomirija, 2015. "Multivariate Stop loss Mixed Erlang Reinsurance risk: Aggregation, Capital allocation and Default risk," Papers 1501.07297, arXiv.org.
    3. Ignatieva, Katja & Landsman, Zinoviy, 2021. "A class of generalised hyper-elliptical distributions and their applications in computing conditional tail risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 437-465.
    4. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    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. Khouzeima Moutanabbir & Hassan Abdelrahman, 2022. "Bivariate Sarmanov Phase-Type Distributions for Joint Lifetimes Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1093-1118, June.
    7. Baishuai Zuo & Chuancun Yin, 2020. "Conditional tail risk expectations for location-scale mixture of elliptical distributions," Papers 2007.09350, arXiv.org.
    8. Raluca Vernic, 2017. "Capital Allocation for Sarmanov’s Class of Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 311-330, March.
    9. Yin, Cuihong & Sheldon Lin, X. & Huang, Rongtan & Yuan, Haili, 2019. "On the consistency of penalized MLEs for Erlang mixtures," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 12-20.

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