Ivica Turkalj, Mohammad Assadsolimani, Markus Braun, Pascal Halffmann, Niklas Hegemann, Sven Kerstan, Janik Maciejewski, Shivam Sharma, Yuanheng Zhou
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引用次数: 0
摘要
在本文中,我们考虑通过使用二次代理模型将偿付能力资本要求(SCR)纳入投资组合优化。偿付能力 II 指令要求保险公司根据下一年的完整损失分布计算偿付能力资本要求。一般来说,这项任务对保险公司来说具有计算上的挑战性(因此在优化投资组合时没有考虑到这一点),因此采用更可行的代理模型为这一计算困难提供了潜在的解决方案。在此,我们提出了一种同样适用于量子计算未来应用的方法。我们利用机器学习技术分析了偿付能力资本比率的二次方近似性。这使得在经典的均值方差分析中更容易考虑偿付能力资本比率。此外,它还允许将问题表述为二次无约束二元优化(QUBO),从而受益于量子计算可能带来的速度提升。我们详细描述了我们的模型以及将其转化为 QUBO 的过程。此外,我们还通过实验研究调查了我们方法的性能。
Quadratic Unconstrained Binary Optimization Approach for Incorporating Solvency Capital into Portfolio Optimization
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.