A difference of convex formulation of value-at-risk constrained optimization

References

• An , LTH . 2000 . An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints . Math. Program. , 87 : 401 – 426 .
   Web of Science ®Google Scholar
• An , LTH , Pham , DT and Thoai , N . 2002 . Combination between global and local methods for solving an optimization problem over the efficient set . Eur. J. Oper. Res. , 142 : 258 – 270 .
   Web of Science ®Google Scholar
• An , LTH and Tao , PD . 2001 . A continuous approach for globally solving linearly constrained quadratic zero-one programming problems . Optimization , 50 : 93 – 120 .
   Web of Science ®Google Scholar
• An , LTH and Tao , PD . 2005 . The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems . Ann. Oper. Res. , 133 : 23 – 46 .
   Web of Science ®Google Scholar
• Artzner , P , Delbaen , F , Eber , JM and Heath , D . 1997 . Thinking coherently . Risk , 10 : 68 – 71 .
   Google Scholar
• Artzner , P , Delbaen , F , Eber , JM and Heath , D . 1999 . Coherent measures of risk . Math. Finance , 9 : 203 – 228 .
   Web of Science ®Google Scholar
• Basak , S and Shapiro , A . 2001 . Value-at-risk management: Optimal policies and asset prices . Rev. Financial Stud. , 14 : 371 – 405 .
   Web of Science ®Google Scholar
• Benati , S and Rizzi , R . 2007 . A mixed integer linear programming formulation of the optimal mean/value-at-risk portfolio problem . Eur. J. Oper. Res. , 176 : 423 – 434 .
   Web of Science ®Google Scholar
• Bomze , IM and Locatelli , M . 2004 . Undominated D.C. decompositions of quadratic functions and applications to branch-and-bound approaches . Comput. Optim. Appl. , 28 : 227 – 245 .
   Web of Science ®Google Scholar
• Campbell , R , Huisman , R and Koedijk , K . 2001 . Optimal portfolio selection in a value-at-risk framework . J. Banking Finance , 25 : 1789 – 1804 .
   Web of Science ®Google Scholar
• Cheon , MS , Ahmed , S and Al-Khayyal , F . 2006 . A branch-reduced-cut algorithm for the global optimization of probabilistically constrained linear programmes . Math. Program. , 108 : 617 – 634 .
   Web of Science ®Google Scholar
• Emmer , S , Klüppelberg , C and Korn , R . 2001 . Optimal portfolios with bounded capital at risk . Math. Finance , 11 : 365 – 384 .
   Web of Science ®Google Scholar
• Fusai , G and Luciano , E . 2001 . Dynamic value at risk under optimal and suboptimal portfolio policies . Eur. J. Oper. Res. , 135 : 249 – 269 .
   Web of Science ®Google Scholar
• Gaivoronski , AA and Pflug , GC . 2005 . Value-at-risk in portfolio optimization: Properties and computational approach . J. Risk , 7 : 1 – 31 .
   Google Scholar
• Gilli , M and Këllezi , E . 2002 . A global optimization heuristic for portfolio choice with VaR and expected shortfall, in Computational Methods in Decision-making. Economics and Finance, E.J. Kontoghiorghes, B. Rustem, and S. Siokos, eds., Applied Optimization, Vol. 74 , 167 – 183 . Dordrecht : Kluwer .
   Google Scholar
• Gilli , M , Këllezi , E and Hysi , H . 2006 . A data-driven optimization heuristic for downside risk minimization . J. Risk , 8 : 1 – 18 .
   Google Scholar
• Hochreiter , R . 2007 . An evolutionary computation approach to scenario-based risk-return portfolio optimization for general risk measures in EvoWorkshops 2007. M. Giacobini, ed., Lecture Notes in Computer Science, Vol. 4448 , 199 – 207 . Berlin : Springer .
   Google Scholar
• Horst , R and Thoai , NV . 1999 . DC programming: Overview . J. Optim. Theory Appl. , 103 : 1 – 43 .
   Web of Science ®Google Scholar
• Horst , R and Tuy , H . 1993 . Global Optimization, , 2nd , Berlin : Springer-Verlag .
   Google Scholar
• Jorion , P . 2000 . Value at Risk: The New Benchmark for Controlling Market Risk , Chicago : McGraw-Hill .
   Google Scholar
• Larsen , N , Mausser , H and Uryasev , S . 2002 . “ Algorithms for optimization of value-at-risk ” . In Financial Engineering, e-Commerce and Supply Chain , Edited by: Pardalos , P and Tsitsiringos , V . 129 – 157 . Norwell : Kluwer Academic Publishers .
   Google Scholar
• Le Thi , HA , Moeini , M and Pham Dinh , T . 2009 . DC programming approach for portfolio optimization under step increasing transaction costs . Optimization , 58 : 267 – 289 .
   Web of Science ®Google Scholar
• Markowitz , HM . 1952 . Portfolio selection . J. Finance , 7 : 77 – 91 .
   Web of Science ®Google Scholar
• McNeil , AJ , Frey , R and Embrechts , P . 2005 . Quantitative Risk Management , Princeton, NJ : Princeton University Press .
   Google Scholar
• Natarajan , K , Pachamanova , D and Sim , M . 2008 . Incorporating asymmetric distributional information in robust value-at-risk optimization . Manag. Sci. , 54 : 573 – 585 .
   Web of Science ®Google Scholar
• Pang , J and Leyffer , S . 2004 . On the global minimization of the value-at-risk . Optim. Methods Softw. , 19 : 611 – 631 .
   Web of Science ®Google Scholar
• Pflug , GC . 2000 . “ Some remarks on the value-at-risk and the conditional value-at-risk ” . In in Probabilistic Constrained Optimization , S.P. Uryasev, ed., Nonconvex Optimization and its Applications , Vol. 49 , 272 – 281 . Dordrecht : Kluwer .
   Google Scholar
• Pflug , GC and Römisch , W . 2007 . Modeling, Measuring and Managing Risk , Singapore : World Scientific .
   Google Scholar
• Pirvu , TA . 2007 . Portfolio optimization under the value-at-risk constraint . Quant. Finance , 7 : 125 – 136 .
   Web of Science ®Google Scholar
• Puelz , A . 2001 . “ Value-at-risk based portfolio optimization ” . In Stochastic Optimization: Algorithms and Applications , Edited by: Uryasev , S and Pardalos , P . 279 – 302 . Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Rockafellar , RT and Uryasev , S . 2000 . Optimization of conditional value-at-risk . J. Risk , 2 : 21 – 41 .
   Google Scholar
• Tapiero , CS . 2005 . Value at risk and inventory control . Eur. J. Oper. Res. , 163 : 769 – 775 .
   Web of Science ®Google Scholar
• Tasche , D and Tibiletti , L . 2004 . Approximations for the value-at-risk approach to risk-return analysis . ICFAI J. Financial Risk Manag. , 1 : 44 – 61 .
   Google Scholar
• Thach , PT and Konno , H . 1997 . On the degree and separability of nonconvexity and applications to optimization problems . Math. Program. , 77 : 23 – 47 .
   Web of Science ®Google Scholar
• Tulli , V and Weinrich , G . 2009 . A firm's optimizing behaviour under a value-at-risk constraint . Optimization , 58 : 213 – 226 .
   Web of Science ®Google Scholar
• Uryasev , S . 2000 . Conditional value-at-risk: Optimization algorithms and applications . Financial Eng. News , 14 : 1 – 5 .
   Google Scholar
• Vehvilinen , I and Keppo , J . 2003 . Managing electricity market price risk . Eur. J. Oper. Res. , 145 : 136 – 147 .
   Web of Science ®Google Scholar