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A Bayesian copula model for stochastic claims reserving

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  • Luca Regis

Abstract

We present a full Bayesian model for assessing the reserve requirement of multiline Non-Life insurance companies. Bayesian models for claims reserving allow to account for expert knowledge in the evaluation of Outstanding Loss Liabilities, allowing the use of additional information at a low cost. This paper combines a standard Bayesian approach for the estimation of marginal distribution for the single Lines of Business for a Non-Life insurance company and a Bayesian copula procedure for the estimation of aggregate reserves. The model we present allows to "mix" own-assessments of dependence between LoBs at a company level and market-wide estimates provided by regulators. We illustrate results for the single lines of business and we compare standard copula aggregation for different copula choices and the Bayesian copula approach.

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  • Luca Regis, 2011. "A Bayesian copula model for stochastic claims reserving," Carlo Alberto Notebooks 227, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:227
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    References listed on IDEAS

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    1. de Alba, Enrique & Nieto-Barajas, Luis E., 2008. "Claims reserving: A correlated Bayesian model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 368-376, December.
    2. Mohamed N. Jouini & Robert T. Clemen, 1996. "Copula Models for Aggregating Expert Opinions," Operations Research, INFORMS, vol. 44(3), pages 444-457, June.
    3. Ioannis Ntzoufras & Petros Dellaportas, 2002. "Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(1), pages 113-125.
    4. Enrique de Alba, 2002. "Bayesian Estimation of Outstanding Claim Reserves," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(4), pages 1-20.
    5. Luciana Dalla Valle, 2009. "Bayesian Copulae Distributions, with Application to Operational Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 11(1), pages 95-115, March.
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    Cited by:

    1. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.

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    More about this item

    Keywords

    stochastic claims reserving; bayesian copulas; solvency capital requirement; loss reserving; bayesian methods;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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