Journal ArticleDOI
Simulating Sensitivities of Conditional Value at Risk
L. Jeff Hong,Guangwu Liu +1 more
TLDR
This paper proves that the CVaR sensitivity can be written as a conditional expectation for general loss distributions, and proposes and demonstrates how to use the estimator to solve optimization problems withCVaR objective and/or constraints, and compares it to a popular linear programming-based algorithm.Abstract:
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.read more
Citations
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Journal ArticleDOI
The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support
Saman Razavi,Anthony Jakeman,Andrea Saltelli,Clémentine Prieur,Bertrand Iooss,Emanuele Borgonovo,Elmar Plischke,Samuele Lo Piano,Takuya Iwanaga,William E. Becker,Stefano Tarantola,Joseph H. A. Guillaume,John D. Jakeman,Hoshin V. Gupta,Nicola Melillo,Giovanni Rabitti,Vincent Chabridon,Qingyun Duan,Xifu Sun,Stefan Smith,R. Sheikholeslami,R. Sheikholeslami,Nasim Hosseini,Masoud Asadzadeh,Arnald Puy,Arnald Puy,Sergei Kucherenko,Holger R. Maier +27 more
TL;DR: A multidisciplinary group of researchers and practitioners revisit the current status of Sensitivity analysis, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems.
Journal ArticleDOI
Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach
L. Jeff Hong,Yi Yang,Liwei Zhang +2 more
TL;DR: It is shown that the solutions of the sequence of approximations converge to a Karush-Kuhn-Tucker (KKT) point of the JCCP under a certain asymptotic regime.
Proceedings Article
Optimizing the CVaR via sampling
TL;DR: A novel sampling-based estimator for the gradient of the CVaR, in the spirit of the likelihood-ratio method is proposed, and the bias of the estimator is analyzed, and it is proved the convergence of a corresponding stochastic gradient descent algorithm to a localCVaR optimum.
Journal ArticleDOI
Monte Carlo Methods for Value-at-Risk and Conditional Value-at-Risk: A Review
TL;DR: Some of the recent developments in Monte Carlo methods used in VaR and CVaR are reviewed, a unified framework to understand them is provided, and their applications in financial risk management are discussed.
References
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Book
Numerical Optimization
Jorge Nocedal,Stephen J. Wright +1 more
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
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Simulation Modeling and Analysis
Averill M. Law,W. David Kelton +1 more
TL;DR: The text is designed for a one-term or two-quarter course in simulation offered in departments of industrial engineering, business, computer science and operations research.
Journal ArticleDOI
Coherent Measures of Risk
TL;DR: In this paper, the authors present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent", and demonstrate the universality of scenario-based methods for providing coherent measures.
Journal ArticleDOI
Optimization of conditional value-at-risk
R. T. Rockafellar,S Uryasev +1 more
TL;DR: In this paper, a new approach to optimize or hedging a portfolio of financial instruments to reduce risk is presented and tested on applications, which focuses on minimizing Conditional Value-at-Risk (CVaR) rather than minimizing Value at Risk (VaR), but portfolios with low CVaR necessarily have low VaR as well.
Book
Probability: Theory and Examples
TL;DR: In this paper, a comprehensive introduction to probability theory covering laws of large numbers, central limit theorem, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion is presented.