Simulating sensitivities of Conditional value at risk

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)281-293
Journal / PublicationManagement Science
Issue number2
Publication statusPublished - Feb 2009
Externally publishedYes


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. © 2009 INFORMS.

Research Area(s)

  • Applications, Portfolio, Simulation, Statistical analysis