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Journal of Industrial and Management Optimization (JIMO)
 

CVaR proxies for minimizing scenario-based Value-at-Risk

Pages: 1109 - 1127, Volume 10, Issue 4, October 2014      doi:10.3934/jimo.2014.10.1109

 
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Helmut Mausser - Quantitative Research, Risk Analytics, Business Analytics, IBM, 185 Spadina Avenue, Toronto, ON M5T2C6, Canada (email)
Oleksandr Romanko - Quantitative Research, Risk Analytics, Business Analytics, IBM, 185 Spadina Avenue, Toronto, ON M5T2C6, Canada (email)

Abstract: Minimizing VaR, as estimated from a set of scenarios, is a difficult integer programming problem. Solving the problem to optimality may demand using only a small number of scenarios, which leads to poor out-of-sample performance. A simple alternative is to minimize CVaR for several different quantile levels and then to select the optimized portfolio with the best out-of-sample VaR. We show that this approach is both practical and effective, outperforming integer programming and an existing VaR minimization heuristic. The CVaR quantile level acts as a regularization parameter and, therefore, its ideal value depends on the number of scenarios and other problem characteristics.

Keywords:  Value-at-risk, conditional value-at-risk, optimization, regularization.
Mathematics Subject Classification:  Primary: 91G10, 91G60, 91B30, 90C05; Secondary: 90C20, 90C11, 65K05.

Received: September 2012;      Revised: October 2013;      Available Online: February 2014.

 References