Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Likelihood ratio gradient estimation for stochastic systems
Communications of the ACM - Special issue on simulation
On a theorem of Danskin with an application to a theorem of Von Neumann-Sion
Nonlinear Analysis: Theory, Methods & Applications
Estimating security price derivatives using simulation
Management Science
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Optimization of Convex Risk Functions
Mathematics of Operations Research
Estimating Quantile Sensitivities
Operations Research
On the controversy over tailweight of distributions
Operations Research Letters
Conditional Monte Carlo Estimation of Quantile Sensitivities
Management Science
Quantile Sensitivity Estimation
NET-COOP '09 Proceedings of the 3rd Euro-NF Conference on Network Control and Optimization
A general framework of importance sampling for value-at-risk and conditional value-at-risk
Winter Simulation Conference
Operations Research Letters
Stochastic kriging for conditional value-at-risk and its sensitivities
Proceedings of the Winter Simulation Conference
Mean-CVaR portfolio selection: A nonparametric estimation framework
Computers and Operations Research
Monte Carlo estimation of value-at-risk, conditional value-at-risk and their sensitivities
Proceedings of the Winter Simulation Conference
A two-level loan portfolio optimization problem
Proceedings of the Winter Simulation Conference
Stochastic kriging with biased sample estimates
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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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.