235
Views
10
CrossRef citations to date
0
Altmetric
Miscellany

Non-smooth optimization methods for computation of the Conditional Value-at-risk and portfolio optimization

&
Pages 459-479 | Received 04 Aug 2005, Accepted 16 Dec 2005, Published online: 29 Oct 2009

References

  • Artzner , P , Delbaen , F , Eber , J-M and Heath , D . 1999 . Coherent measures of risk. . Mathematical Finance , 9 : 203 – 228 .
  • Artzner , P , Delbaen , F , Eber , J-M and Heath , D . 1997 . Thinking coherently. . Risk , 10 : 68 – 71 .
  • Acerbi , C and Tasche , D . 2002 . Expected shortfall: a natural coherent alternative to value at risk. . Economic Notes , 31 : 379 – 388 .
  • Rockafellar , RT and Uryasev , S . 2000 . Optimization of conditional value-at-risk. . Journal of Risk , 2 : 21 – 41 .
  • Rockafellar , RT and Uryasev , S . 2002 . Conditional value-at-risk for general loss distributions. . Journal of Banking and Finance , 26 : 1443 – 1471 .
  • Bagirov , A . 2002 . A method for minimization of quasidifferentiable functions. . Optimization Methods and Software , 17 : 31 – 60 .
  • Lüthi , H-J and Doege , J . 2005 . Convex risk measures for portfolio optimization and concepts of flexibility. . Mathematical Programming , 104 : 541 – 559 .
  • Yamai , Y and Yoshiba , T . 2002 . On the validity of value-at-risk: comparative analyses with expected shortfall. . Monetary and Economic Studies , 20 : 57 – 85 .
  • Mausser , H and Rosen , D . 1999 . Efficient risk/return frontiers for credit risk. . Algo Research Quarterly , 2 : 35 – 47 .
  • Clarke , FH . 1983 . Optimization and Nonsmooth Analysis , New York : John Wiley .
  • Bagirov , A . 1999 . Derivative-free methods for unconstrained nonsmooth optimization and its numerical analysis. . Journal Investigacao Operacional , 19 : 75 – 93 .
  • Bagirov , A . 2003 . Continuous subdifferential approximations and their applications. . Journal of Mathematical Sciences , 115 : 2567 – 2609 .
  • Bagirov , A . 1999 . “ Minimization methods for one class of nonsmooth functions and calculation of semi-equilibrium prices ” . In Progress in Optimization: Contribution from Australasia , Edited by: Eberhard , A . 147 – 175 . Dordrecht : Kluwer .
  • Bagirov , A and Gasanov , A . 1995 . A method of approximating a quasidifferential. . Russian Journal of Computational Mathematics and Mathematical Physics , 35 : 403 – 409 .
  • Wolfe , PH . 1976 . Finding the nearest point in a polytope. . Mathematical Programming , 11 : 128 – 149 .
  • Markowitz , HM . 1952 . Portfolio selection. . Journal of Finance , 7 : 77 – 91 .
  • Barndorff-Nielsen , OE . 1977 . Exponentially decreasing distributions for the logarithm of particle size. . Proceeding of Royal Society of London A , 353 : 401 – 419 .
  • Eberlein , E and Keller , U . 1995 . Hyperbolic distributions in finance. . Bernoulli , 1 : 281 – 299 .
  • Bauer , C . 2000 . Value at risk using hyperbolic distributions. . Journal of Economics and Business , 52 : 455 – 467 .
  • Prause , K . 1999 . “ The Generalized Hyperbolic Model: Estimation. Financial Derivatives and Risk Measures ” . In PhD thesis , Albert-Ludwigs Universität .
  • Notebaert , P , Eikland , K and Berkelaar , M . 2004 . Lp_solve, http://groups.yahoo.com/group/lp_solve/
  • Makhorin , A . 2004 . Gnu linear programming kit, http://www.gnu.org/software/glpk/glpk.html
  • Kiwiel , KC . 1985 . “ Methods of Descent of Nondifferentiable Optimization ” . In Vol. 1133 of Lecture Notes in Mathematics , Berlin : Springer .
  • Beliakov , G , Bagirov , A and Monsalve , JE . 2003 . “ Parallelization of the discrete gradient method of non-smooth optimization and its applications ” . In Proceedings of the 3rd International Conference on Computational Science , Vol. 3 , 592 – 601 . Heidelberg : Springer-Verlag . Springer-Verlag Lecture Notes in Computer Science (LNCS)
  • Hall , J . 2005 . Towards a practical parallelisation of the simplex method. . Computational Management Science , (Submitted)
  • Hall , J and McKinnon , K . 1998 . Asynplex, an asynchronous parallel revised simplex method algorithm. . Annals of Operations Research , 81 : 27 – 49 .
  • Amdahl , GM . 1967 . “ Validity of the single-processor approach to achieving large scale computing capabilities ” . In AFIPS Conference Proceedings , Vol. 30 , 483 – 485 . AFIPS Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.