Article2009

Constructing Risk Measures from Uncertainty Sets

Karthik Natarajan · Dessislava A. Pachamanova · Melvyn Sim

165 citations0/0 files storedOperations Research

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Risk and Portfolio Optimization Financial Risk and Volatility Modeling Advanced Optimization Algorithms Research

Abstract

We illustrate the correspondence between uncertainty sets in robust optimization and some popular risk measures in finance and show how robust optimization can be used to generalize the concepts of these risk measures. We also show that by using properly defined uncertainty sets in robust optimization models, one can construct coherent risk measures and address the issue of the computational tractability of the resulting formulations. Our results have implications for efficient portfolio optimization under different measures of risk.

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References

1999Coherent Measures of Risk 2000Optimization of conditional value-at-risk 1959Portfolio Selection: Efficient Diversification of Investments 2004The Price of Robustness 1958Liquidity Preference as Behavior Towards Risk 2002Conditional value-at-risk for general loss distributions 1962Portfolio Selection: Efficient Diversification of Investments.2009Robust Optimization

Cited by

2010A Soft Robust Model for Optimization Under Ambiguity 2011Theory and Applications of Robust Optimization 2012Worst-Case Value at Risk of Nonlinear Portfolios 2009Portfolio selection under distributional uncertainty: A relative robust CVaR approach 2018Risk-Averse Two-Stage Stochastic Program with Distributional Ambiguity 2017Stability advances in robust portfolio optimization under parallelepiped uncertainty 2012Inverse Optimization: A New Perspective on the Black-Litterman Model

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