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Risk- and value-based management for non-life insurers under solvency constraints

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  • Eckert, Johanna
  • Gatzert, Nadine

Abstract

The aim of this paper is to study optimal risk- and value-based management decisions regarding a non-life insurer's investment strategy by maximizing shareholder value based on preference functions, while simultaneously controlling for the ruin probability. We thereby extend previous work by deriving analytical solutions and by explicitly accounting for the policyholders’ willingness to pay depending on their risk sensitivity based on the insurer's reported solvency status, which will be of great relevance under Solvency II. We further investigate the impact of the risk-free interest rate, (non-linear) dependencies between assets and liabilities, distributional assumptions as well as reinsurance. One main finding is that the consideration of default-risk-driven premiums is vital for optimal management decisions, since, e.g., the target ruin probability implying a higher shareholder value differs for various risk sensitivities of the policyholders. Furthermore, in the present setting, proportional reinsurance increases shareholder value only for non-risk sensitive policyholders.

Suggested Citation

  • Eckert, Johanna & Gatzert, Nadine, 2018. "Risk- and value-based management for non-life insurers under solvency constraints," European Journal of Operational Research, Elsevier, vol. 266(2), pages 761-774.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:761-774
    DOI: 10.1016/j.ejor.2017.10.030
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    3. Paulusch, Joachim & Schlütter, Sebastian, 2022. "Sensitivity-implied tail-correlation matrices," Journal of Banking & Finance, Elsevier, vol. 134(C).
    4. Boonen, Tim J. & Jiang, Wenjun, 2022. "A marginal indemnity function approach to optimal reinsurance under the Vajda condition," European Journal of Operational Research, Elsevier, vol. 303(2), pages 928-944.
    5. Supper, Hendrik & Irresberger, Felix & Weiß, Gregor, 2020. "A comparison of tail dependence estimators," European Journal of Operational Research, Elsevier, vol. 284(2), pages 728-742.
    6. Leung, Melvern & Li, Youwei & Pantelous, Athanasios A. & Vigne, Samuel A., 2021. "Bayesian Value-at-Risk backtesting: The case of annuity pricing," European Journal of Operational Research, Elsevier, vol. 293(2), pages 786-801.
    7. Dina Manolache Aurora Elena, 2019. "Stress and scenario tests in the context of a Romanian non-life insurance company," Proceedings of the International Conference on Business Excellence, Sciendo, vol. 13(1), pages 149-161, May.

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