Simulating Sensitivities of Conditional Value at Risk
研究如何用蒙特卡洛模拟估计条件风险价值（CVaR）的敏感性，提出一个估计量并分析其渐近性质，数值实验表明该估计量有效，可用于含CVaR目标的优化问题。
Conditional value at risk (CVaR) is both a coherent risk measure and a natural risk statistic. It is often used to measure the risk associated with large losses. In this paper, we study how to estimate the sensitivities of CVaR using Monte Carlo simulation. We first prove that the CVaR sensitivity can be written as a conditional expectation for general loss distributions. We then propose an estimator of the CVaR sensitivity and analyze its asymptotic properties. The numerical results show that the estimator works well. Furthermore, we demonstrate how to use the estimator to solve optimization problems with CVaR objective and/or constraints, and compare it to a popular linear programming-based algorithm.