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

Ivica Turkalj (), Mohammad Assadsolimani, Markus Braun, Pascal Halffmann, Niklas Hegemann, Sven Kerstan, Janik Maciejewski, Shivam Sharma and Yuanheng Zhou
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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

Risks, 2024, vol. 12, issue 2, 1-17

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.

Keywords: solvency II; quadratic unconstrained binary optimization; portfolio optimization; proxy modeling (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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