计算信贷组合风险贡献的量子算法
Quantum algorithm for calculating risk contributions in a credit portfolio
摘要：
金融是量子计算产业化应用的最有前景的领域之一。特别是，已经提出了用于计算风险度量的量子算法，例如信用组合的风险价值和条件风险价值。在本文中，我们专注于信用风险管理的另一个问题，计算的风险贡献，量化的风险集中在子组的投资组合。基于目前多个期望值同时估计的量子算法，提出了信用风险贡献度的计算方法。我们还评估了所提出的方法的查询复杂性，并看到它的规模为$\widetilde{O}\left(\sqrt{N_{\rm gr}}/ε\right)$的子群数$N_{\rm gr}$和准确性$ε$，与经典的方法相比，$\widetilde{O}\left(\log(N_{\rm gr})/ε^2\right)$复杂性。这意味着，对于细分子群的风险贡献计算，量子方法的优势与整个投资组合的风险度量计算相比有所减少。尽管如此，量子方法在高精度计算中可能是有利的，并且实际上在某些实际上合理的设置中产生比经典方法更低的复杂性。
英文摘要：
Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have been proposed. In this paper, we focus on another problem in credit risk management, calculation of risk contributions, which quantify the concentration of the risk on subgroups in the portfolio. Based on the recent quantum algorithm for simultaneous estimation of multiple expected values, we propose the method for credit risk contribution calculation. We also evaluate the query complexity of the proposed method and see that it scales as $\widetilde{O}\left(\sqrt{N_{\rm gr}}/ε\right)$ on the subgroup number $N_{\rm gr}$ and the accuracy $ε$, in contrast with the classical method with $\widetilde{O}\left(\log(N_{\rm gr})/ε^2\right)$ complexity. This means that, for calculation of risk contributions of finely divided subgroups, the advantage of the quantum method is reduced compared with risk measure calculation for the entire portfolio. Nevertheless, the quantum method can be advantageous in high-accuracy calculation, and in fact yield less complexity than the classical method in some practically plausible setting.
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