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A Copula-Based Bivariate Composite Model for Modelling Claim Costs

Author

Listed:
  • Girish Aradhye

    (Department of Statistics, Central University of Rajasthan, Ajmer 305817, India
    These authors contributed equally to this work.)

  • George Tzougas

    (Maxwell Institute for Mathematical Sciences, Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK)

  • Deepesh Bhati

    (Department of Statistics, Central University of Rajasthan, Ajmer 305817, India
    These authors contributed equally to this work.)

Abstract

This paper aims to develop a new family of bivariate distributions for modelling different types of claims and their associated costs jointly in a flexible manner. The proposed bivariate distributions can be viewed as a continuous copula distribution paired with two marginals based on composite distributions. For expository purposes, the details of one of the proposed bivarite composite distributions is provided. The dependence measures for the resulting bivariate copula-based composite distribution are studied, and its fitting is compared with other bivariate composite distributions and existing bivariate distributions. The parameters of the proposed bivariate composite model are estimated via the inference functions for margins (IFM) method. The suitability of the proposed bivariate distribution is examined using two real-world insurance datasets, namely the motor third-party liability (MTPL) insurance dataset and Danish fire insurance dataset.

Suggested Citation

  • Girish Aradhye & George Tzougas & Deepesh Bhati, 2024. "A Copula-Based Bivariate Composite Model for Modelling Claim Costs," Mathematics, MDPI, vol. 12(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:350-:d:1323725
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    References listed on IDEAS

    as
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    2. Bettina Grün & Tatjana Miljkovic, 2019. "Extending composite loss models using a general framework of advanced computational tools," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(8), pages 642-660, September.
    3. Wang, Yinzhi & Hobæk Haff, Ingrid & Huseby, Arne, 2020. "Modelling extreme claims via composite models and threshold selection methods," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 257-268.
    4. S. Nadarajah & S.A.A. Bakar, 2014. "New composite models for the Danish fire insurance data," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2014(2), pages 180-187.
    5. Abu Bakar, S.A. & Hamzah, N.A. & Maghsoudi, M. & Nadarajah, S., 2015. "Modeling loss data using composite models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 146-154.
    6. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
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