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Portfolio optimization under Solvency II

Author

Listed:
  • Marcos Escobar

    (Western University)

  • Paul Kriebel

    (Technical University of Munich)

  • Markus Wahl

    (Technical University of Munich)

  • Rudi Zagst

    (Technical University of Munich)

Abstract

In the current low interest-rate and highly-regulated environment investing capital efficiently is one of the most important challenges insurance companies face. Certain quantitative parts of regulatory requirements (e.g. Solvency II capital requirements) result in constraints on the investment strategies. This paper mathematically describes the implications of Solvency II constraints on the investment strategies of insurance companies in an expected utility framework with a focus on the market risk module. For this constrained expected utility problem, we define a two-step approach that leads to closed-form approximations for the optimal investment strategies. This proposal circumvents the technical difficulties encountered when applying the convex duality approach or the theory of viscosity solutions. The investment strategies found using the two-step approach can be understood as the optimal investment strategies for constraint problems according to Solvency II. The impact of such constraints on the asset allocation and the performance of these strategies is assessed in a numerical case study.

Suggested Citation

  • Marcos Escobar & Paul Kriebel & Markus Wahl & Rudi Zagst, 2019. "Portfolio optimization under Solvency II," Annals of Operations Research, Springer, vol. 281(1), pages 193-227, October.
    • Handle: RePEc:spr:annopr:v:281:y:2019:i:1:d:10.1007_s10479-018-2835-x
    DOI: 10.1007/s10479-018-2835-x
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    References listed on IDEAS

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    1. Thomas Steffen, 2008. "Solvency II and the Work of CEIOPS," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 33(1), pages 60-65, January.
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    4. Nadine Gatzert & Hannah Wesker, 2012. "A Comparative Assessment of Basel II/III and Solvency II," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 37(3), pages 539-570, July.
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    10. Katharina Fischer & Sebastian Schlütter, 2015. "Optimal Investment Strategies for Insurance Companies when Capital Requirements are Imposed by a Standard Formula*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 40(1), pages 15-40, March.
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    Cited by:

    1. Escobar-Anel, Marcos & Havrylenko, Yevhen & Kschonnek, Michel & Zagst, Rudi, 2022. "Decrease of capital guarantees in life insurance products: Can reinsurance stop it?," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 14-40.
    2. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    3. Kolos Csaba 'Agoston & Veronika Varga, 2024. "Bertrand oligopoly in insurance markets with Value at Risk Constraints," Papers 2404.17915, arXiv.org.
    4. Kerstin Dächert & Ria Grindel & Elisabeth Leoff & Jonas Mahnkopp & Florian Schirra & Jörg Wenzel, 2022. "Multicriteria asset allocation in practice," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 349-373, June.
    5. Kerstin Dachert & Ria Grindel & Elisabeth Leoff & Jonas Mahnkopp & Florian Schirra & Jorg Wenzel, 2021. "Multicriteria asset allocation in practice," Papers 2103.10958, arXiv.org.

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