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Quadratic Unconstrained Binary Optimization Approach for Incorporating Solvency Capital into Portfolio Optimization

Author

Listed:
  • Ivica Turkalj

    (Department of Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

  • Mohammad Assadsolimani

    (DZ BANK AG, Platz der Republik, 60325 Frankfurt am Main, Germany)

  • Markus Braun

    (JoS QUANTUM GmbH, Platz der Einheit 2, 60327 Frankfurt Am Main, Germany)

  • Pascal Halffmann

    (Department of Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

  • Niklas Hegemann

    (JoS QUANTUM GmbH, Platz der Einheit 2, 60327 Frankfurt Am Main, Germany)

  • Sven Kerstan

    (JoS QUANTUM GmbH, Platz der Einheit 2, 60327 Frankfurt Am Main, Germany)

  • Janik Maciejewski

    (R+V Lebensversicherung AG, Raiffeisenplatz 2, 65189 Wiesbaden, Germany)

  • Shivam Sharma

    (Department of Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

  • Yuanheng Zhou

    (JoS QUANTUM GmbH, Platz der Einheit 2, 60327 Frankfurt Am Main, Germany)

Abstract

In this paper, we consider the inclusion of the solvency capital requirement (SCR) into portfolio optimization by the use of a quadratic proxy model. The Solvency II directive requires insurance companies to calculate their SCR based on the complete loss distribution for the upcoming year. Since this task is, in general, computationally challenging for insurance companies (and therefore, not taken into account during portfolio optimization), employing more feasible proxy models provides a potential solution to this computational difficulty. Here, we present an approach that is also suitable for future applications in quantum computing. We analyze the approximability of the solvency capital ratio in a quadratic form using machine learning techniques. This allows for an easier consideration of the SCR in the classical mean-variance analysis. In addition, it allows the problem to be formulated as a quadratic unconstrained binary optimization (QUBO), which benefits from the potential speedup of quantum computing. We provide a detailed description of our model and the translation into a QUBO. Furthermore, we investigate the performance of our approach through experimental studies.

Suggested Citation

  • Ivica Turkalj & Mohammad Assadsolimani & Markus Braun & Pascal Halffmann & Niklas Hegemann & Sven Kerstan & Janik Maciejewski & Shivam Sharma & Yuanheng Zhou, 2024. "Quadratic Unconstrained Binary Optimization Approach for Incorporating Solvency Capital into Portfolio Optimization," Risks, MDPI, vol. 12(2), pages 1-17, January.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:2:p:23-:d:1328788
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    References listed on IDEAS

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    1. 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.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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