论文标题
用于计算信用组合中风险贡献的量子算法
Quantum algorithm for calculating risk contributions in a credit portfolio
论文作者
论文摘要
金融是量子计算工业应用的有前途领域之一。特别是，已经提出了用于计算风险措施的量子算法，例如风险的价值和信用组合风险的条件价值。在本文中，我们专注于信用风险管理中的另一个问题，风险贡献的计算，这些问题量化了投资组合中亚组的风险集中。基于最近对多个期望值估计的量子算法，我们提出了信用风险贡献计算的方法。我们还评估了提出方法的查询复杂性，并确保它缩放为$ \ widetilde {o} \ left（\ sqrt {\ sqrt {n _ {\ rm gr}}/ε\ right）$ in Number $ n _ {\ rm gr} $及其精度与准确的$ qultical $ n _ { $ \ widetilde {o} \ left（\ log（n _ {\ rm gr}）/ε^2 \ right）$复杂度。这意味着，为了计算细分亚组的风险贡献，与整个投资组合的风险度量计算相比，量子方法的优势降低了。然而，量子方法在高准确性计算中可能是有利的，实际上，在某些实际上合理的环境中，比经典方法产生的复杂性较小。
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.
