论文标题
用于在投资组合风险测量中应用的嵌套模拟的样品回收
Sample Recycling for Nested Simulation with Application in Portfolio Risk Measurement
论文作者
论文摘要
嵌套模拟是解决运营研究和金融工程中嵌套估计问题的自然方法。外部层次模拟会生成外部场景，并且在每个外部场景中运行内部层面模拟，以估计相应的条件期望。然后，将产生的条件期望样本用于估计感兴趣的不同风险度量。尽管具有灵活性，但嵌套的模拟因其沉重的计算负担而臭名昭著。我们介绍了一种新型的模拟程序，该过程重复了内部模拟输出，以提高解决嵌套估计问题的效率和准确性。我们分析了由此产生的估计器的偏差，方差和MSE的收敛速率。此外，提出了中央限制定理和方差估计器，这导致了嵌套的感兴趣风险度量渐近有效的置信区间。我们就两个财务风险衡量问题进行数值研究。我们的数值研究表明，渐近分析的结果一致，并表明所提出的方法的表现优于标准嵌套模拟和用于嵌套估计问题的最先进的回归方法。
Nested simulation is a natural approach to tackle nested estimation problems in operations research and financial engineering. The outer-level simulation generates outer scenarios and the inner-level simulations are run in each outer scenario to estimate the corresponding conditional expectation. The resulting sample of conditional expectations is then used to estimate different risk measures of interest. Despite its flexibility, nested simulation is notorious for its heavy computational burden. We introduce a novel simulation procedure that reuses inner simulation outputs to improve efficiency and accuracy in solving nested estimation problems. We analyze the convergence rates of the bias, variance, and MSE of the resulting estimator. In addition, central limit theorems and variance estimators are presented, which lead to asymptotically valid confidence intervals for the nested risk measure of interest. We conduct numerical studies on two financial risk measurement problems. Our numerical studies show consistent results with the asymptotic analysis and show that the proposed approach outperforms the standard nested simulation and a state-of-art regression approach for nested estimation problems.
