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Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks

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  • Gareth W. Peters

    (Department of Statistical Science, University College London, London WC1E 6BT, UK
    Oxford-Man Institute, Oxford University, Oxford OX1 2JD, UK
    System Risk Center, London School of Economics, London WC2A 2AE, UK)

  • Rodrigo S. Targino

    (Fundação Getulio Vargas, Escola de Matemática Aplicada, Botafogo, RJ 22250-040, Brazil)

  • Mario V. Wüthrich

    (RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland)

Abstract

The main objective of this work is to develop a detailed step-by-step guide to the development and application of a new class of efficient Monte Carlo methods to solve practically important problems faced by insurers under the new solvency regulations. In particular, a novel Monte Carlo method to calculate capital allocations for a general insurance company is developed, with a focus on coherent capital allocation that is compliant with the Swiss Solvency Test. The data used is based on the balance sheet of a representative stylized company. For each line of business in that company, allocations are calculated for the one-year risk with dependencies based on correlations given by the Swiss Solvency Test. Two different approaches for dealing with parameter uncertainty are discussed and simulation algorithms based on (pseudo-marginal) Sequential Monte Carlo algorithms are described and their efficiency is analysed.

Suggested Citation

  • Gareth W. Peters & Rodrigo S. Targino & Mario V. Wüthrich, 2017. "Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks," Risks, MDPI, vol. 5(4), pages 1-51, September.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:4:p:53-:d:112832
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    References listed on IDEAS

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    Cited by:

    1. Koike, Takaaki & Saporito, Yuri & Targino, Rodrigo, 2022. "Avoiding zero probability events when computing Value at Risk contributions," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 173-192.
    2. Claus Baumgart & Johannes Krebs & Robert Lempertseder & Oliver Pfaffel, 2019. "Quantifying Life Insurance Risk using Least-Squares Monte Carlo," Papers 1910.03951, arXiv.org.
    3. Albert Cohen, 2018. "Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance," Risks, MDPI, vol. 6(1), pages 1-3, January.

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