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CVaR proxies for minimizing scenario-based Value-at-Risk
1. | Quantitative Research, Risk Analytics, Business Analytics, IBM, 185 Spadina Avenue, Toronto, ON M5T2C6, Canada, Canada |
References:
[1] |
C. Acerbi and D. Tasche, Expected Shortfall: A natural coherent alternative to Value at Risk, Economic Notes, 31 (2002), 379-388.
doi: 10.1111/1468-0300.00091. |
[2] |
C. Acerbi and D. Tasche, On the coherence of expected shortfall, Journal of Banking & Finance, 26 (2002), 1487-1503.
doi: 10.1016/S0378-4266(02)00283-2. |
[3] |
B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, A First Course in Order Statistics, SIAM Publishers, Philadelphia, PA, 2008.
doi: 10.1137/1.9780898719062. |
[4] |
P. Artzner, F. Delbaen, J.-M. Eber and D. Heath, Coherent measures of risk, Mathematical Finance, 9 (1999), 203-228.
doi: 10.1111/1467-9965.00068. |
[5] |
V. Brazauskas, B. L. Jones, M. L. Puri and R. Zitikis, Estimating conditional tail expectation with actuarial applications in view, Journal of Statistical Planning and Inference, 138 (2008), 3590-3604.
doi: 10.1016/j.jspi.2005.11.011. |
[6] |
J. Daníelsson, B. N. Jorgensen, G. Samorodnitsky, M. Sarma and C. G. de Vries, Subadditivity re-examined: The case for Value-at-Risk, preprint, London School of Economics, 2005. |
[7] |
V. DeMiguel, L. Garlappi, F. J. Nogales and R. Uppal, A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms, Management Science, 55 (2009), 798-812.
doi: 10.1287/mnsc.1080.0986. |
[8] |
K. Høyland, M. Kaut and S. W. Wallace, A heuristic for moment-matching scenario generation, Computational Optimization and Applications, 24 (2003), 169-185.
doi: 10.1023/A:1021853807313. |
[9] |
N. Larsen, H. Mausser and S. Uryasev, Algorithms for optimization of Value-at-Risk, in Financial Engineering, E-commerce and Supply Chain (eds. P. Pardalos and V. K. Tsitsiringos), Kluwer Academic Publishers, Norwell, MA, (2002), 19-46.
doi: 10.1007/978-1-4757-5226-7_2. |
[10] |
J. Luedtke and S. Ahmed, A sample approximation approach for optimization with probabilistic constraints, SIAM Journal on Optimization, 19 (2008), 674-699.
doi: 10.1137/070702928. |
[11] |
H. Mausser and O. Romanko, Bias, exploitation and proxies in scenario-based risk minimization, Optimization, 61 (2012), 1191-1219.
doi: 10.1080/02331934.2012.684795. |
[12] |
H. Mausser and D. Rosen, Efficient risk/return frontiers for credit risk, Journal of Risk Finance, 2 (2000), 66-78.
doi: 10.1108/eb022948. |
[13] |
K. Natarajan, D. Pachamanova and M. Sim, Incorporating asymmetric distribution information in robust value-at-risk optimization, Management Science, 54 (2008), 573-585.
doi: 10.1287/mnsc.1070.0769. |
[14] |
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM Journal on Optimization, 17 (2006), 969-996.
doi: 10.1137/050622328. |
[15] |
B. K. Pagnoncelli, S. Ahmed and A. Shapiro, Computational study of a chance constrained portfolio selection problem, Optimization Online, 2008. Available from: http://www.optimization-online.org/DB_HTML/2008/02/1899.html. |
[16] |
B. K. Pagnoncelli, S. Ahmed and A. Shapiro, Sample average approximation method for chance constrained programming: Theory and applications, Journal of Optimization Theory and Applications, 142 (2009), 399-416.
doi: 10.1007/s10957-009-9523-6. |
[17] |
R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, Journal of Risk, 2 (2000), 21-41. |
[18] |
R. T. Rockafellar and S. Uryasev, Conditional value-at-risk for general loss distributions, Journal of Banking & Finance, 26 (2002), 1443-1471.
doi: 10.1016/S0378-4266(02)00271-6. |
[19] |
D. Wuertz and H. Katzgraber, Precise Finite-Sample Quantiles of the Jarque-Bera Adjusted Lagrange Multiplier Test, MPRA Paper No. 19155, University of Munich, 2009. Available from: http://mpra.ub.uni-muenchen.de/19155/. |
show all references
References:
[1] |
C. Acerbi and D. Tasche, Expected Shortfall: A natural coherent alternative to Value at Risk, Economic Notes, 31 (2002), 379-388.
doi: 10.1111/1468-0300.00091. |
[2] |
C. Acerbi and D. Tasche, On the coherence of expected shortfall, Journal of Banking & Finance, 26 (2002), 1487-1503.
doi: 10.1016/S0378-4266(02)00283-2. |
[3] |
B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, A First Course in Order Statistics, SIAM Publishers, Philadelphia, PA, 2008.
doi: 10.1137/1.9780898719062. |
[4] |
P. Artzner, F. Delbaen, J.-M. Eber and D. Heath, Coherent measures of risk, Mathematical Finance, 9 (1999), 203-228.
doi: 10.1111/1467-9965.00068. |
[5] |
V. Brazauskas, B. L. Jones, M. L. Puri and R. Zitikis, Estimating conditional tail expectation with actuarial applications in view, Journal of Statistical Planning and Inference, 138 (2008), 3590-3604.
doi: 10.1016/j.jspi.2005.11.011. |
[6] |
J. Daníelsson, B. N. Jorgensen, G. Samorodnitsky, M. Sarma and C. G. de Vries, Subadditivity re-examined: The case for Value-at-Risk, preprint, London School of Economics, 2005. |
[7] |
V. DeMiguel, L. Garlappi, F. J. Nogales and R. Uppal, A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms, Management Science, 55 (2009), 798-812.
doi: 10.1287/mnsc.1080.0986. |
[8] |
K. Høyland, M. Kaut and S. W. Wallace, A heuristic for moment-matching scenario generation, Computational Optimization and Applications, 24 (2003), 169-185.
doi: 10.1023/A:1021853807313. |
[9] |
N. Larsen, H. Mausser and S. Uryasev, Algorithms for optimization of Value-at-Risk, in Financial Engineering, E-commerce and Supply Chain (eds. P. Pardalos and V. K. Tsitsiringos), Kluwer Academic Publishers, Norwell, MA, (2002), 19-46.
doi: 10.1007/978-1-4757-5226-7_2. |
[10] |
J. Luedtke and S. Ahmed, A sample approximation approach for optimization with probabilistic constraints, SIAM Journal on Optimization, 19 (2008), 674-699.
doi: 10.1137/070702928. |
[11] |
H. Mausser and O. Romanko, Bias, exploitation and proxies in scenario-based risk minimization, Optimization, 61 (2012), 1191-1219.
doi: 10.1080/02331934.2012.684795. |
[12] |
H. Mausser and D. Rosen, Efficient risk/return frontiers for credit risk, Journal of Risk Finance, 2 (2000), 66-78.
doi: 10.1108/eb022948. |
[13] |
K. Natarajan, D. Pachamanova and M. Sim, Incorporating asymmetric distribution information in robust value-at-risk optimization, Management Science, 54 (2008), 573-585.
doi: 10.1287/mnsc.1070.0769. |
[14] |
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM Journal on Optimization, 17 (2006), 969-996.
doi: 10.1137/050622328. |
[15] |
B. K. Pagnoncelli, S. Ahmed and A. Shapiro, Computational study of a chance constrained portfolio selection problem, Optimization Online, 2008. Available from: http://www.optimization-online.org/DB_HTML/2008/02/1899.html. |
[16] |
B. K. Pagnoncelli, S. Ahmed and A. Shapiro, Sample average approximation method for chance constrained programming: Theory and applications, Journal of Optimization Theory and Applications, 142 (2009), 399-416.
doi: 10.1007/s10957-009-9523-6. |
[17] |
R. T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, Journal of Risk, 2 (2000), 21-41. |
[18] |
R. T. Rockafellar and S. Uryasev, Conditional value-at-risk for general loss distributions, Journal of Banking & Finance, 26 (2002), 1443-1471.
doi: 10.1016/S0378-4266(02)00271-6. |
[19] |
D. Wuertz and H. Katzgraber, Precise Finite-Sample Quantiles of the Jarque-Bera Adjusted Lagrange Multiplier Test, MPRA Paper No. 19155, University of Munich, 2009. Available from: http://mpra.ub.uni-muenchen.de/19155/. |
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