论文标题
量子风险分析：超越（有条件的）价值风险
Quantum Risk Analysis: Beyond (Conditional) Value-at-Risk
论文作者
论文摘要
风险措施是衡量公司储备金的充分性的重要关键数字。实际上，最常见的风险度量是风险价值（VAR）和有条件的危险价值（CVAR）。最近，引入了基于量子的算法来计算它们。这些过程基于所谓的量子幅度估计算法，该算法与基于蒙特卡洛的经典方法相比，导致二次速度提高。基于这些思想，我们构建了基于量子的算法来计算VAR和CVAR的替代方案，即危险的期望值（EVAR）和风险范围值（RVAR）。我们构建量子算法来计算它们。这些算法基于量子幅度估计。在案例研究中，我们将其性能与用于VAR和CVAR的基于量子的算法进行了比较。我们发现，所有算法在量子模拟器上的表现都很好。此外，EVAR和VAR的计算在实际量子设备上具有稳定性。 CVAR和RVAR并非如此。
Risk measures are important key figures to measure the adequacy of the reserves of a company. The most common risk measures in practice are Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Recently, quantum-based algorithms are introduced to calculate them. These procedures are based on the so-called quantum amplitude estimation algorithm which lead to a quadratic speed up compared to classical Monte-Carlo based methods. Based on these ideas, we construct quantum-based algorithms to calculate alternatives for VaR and CVaR, namely the Expectile Value-at-Risk (EVaR) and the Range Value-at-Risk (RVaR). We construct quantum algorithms to calculate them. These algorithms are based on quantum amplitude estimation. In a case study, we compare their performance with the quantum-based algorithms for VaR and CVaR. We find that all of the algorithms perform sufficiently well on a quantum simulator. Further, the calculations of EVaR and VaR are robust against noise on a real quantum device. This is not the case for CVaR and RVaR.
