IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v216y2012i2p376-385.html
   My bibliography  Save this article

Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization

Author

Listed:
  • Meskarian, Rudabeh
  • Xu, Huifu
  • Fliege, Jörg

Abstract

Inspired by the successful applications of the stochastic optimization with second order stochastic dominance (SSD) model in portfolio optimization, we study new numerical methods for a general SSD model where the underlying functions are not necessarily linear. Specifically, we penalize the SSD constraints to the objective under Slater’s constraint qualification and then apply the well known stochastic approximation (SA) method and the level function method to solve the penalized problem. Both methods are iterative: the former requires to calculate an approximate subgradient of the objective function of the penalized problem at each iterate while the latter requires to calculate a subgradient. Under some moderate conditions, we show that w.p.1 the sequence of approximated solutions generated by the SA method converges to an optimal solution of the true problem. As for the level function method, the convergence is deterministic and in some cases we are able to estimate the number of iterations for a given precision. Both methods are applied to portfolio optimization problem where the return functions are not necessarily linear and some numerical test results are reported.

Suggested Citation

  • Meskarian, Rudabeh & Xu, Huifu & Fliege, Jörg, 2012. "Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 216(2), pages 376-385.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:2:p:376-385
    DOI: 10.1016/j.ejor.2011.07.044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171100676X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2011.07.044?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Baker, Barrie M. & Sheasby, Janice, 1999. "Accelerating the convergence of subgradient optimisation," European Journal of Operational Research, Elsevier, vol. 117(1), pages 136-144, August.
    2. Dupacova, Jitka & Gaivoronski, Alexei & Kos, Zdenek & Szantai, Tamas, 1991. "Stochastic programming in water management: A case study and a comparison of solution techniques," European Journal of Operational Research, Elsevier, vol. 52(1), pages 28-44, May.
    3. Ermoliev, Yuri M. & Norkin, Vladimir I., 1997. "On nonsmooth and discontinuous problems of stochastic systems optimization," European Journal of Operational Research, Elsevier, vol. 101(2), pages 230-244, September.
    4. H. Xu, 2001. "Level Function Method for Quasiconvex Programming," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 407-437, February.
    5. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Post, Thierry, 2016. "Standard Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1009-1020.
    2. Branda, Martin, 2015. "Diversification-consistent data envelopment analysis based on directional-distance measures," Omega, Elsevier, vol. 52(C), pages 65-76.
    3. Yu Mei & Zhiping Chen & Jia Liu & Bingbing Ji, 2022. "Multi-stage portfolio selection problem with dynamic stochastic dominance constraints," Journal of Global Optimization, Springer, vol. 83(3), pages 585-613, July.
    4. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    5. Martin Branda, 2013. "On relations between chance constrained and penalty function problems under discrete distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 265-277, April.
    6. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.
    7. Martin Branda & Miloš Kopa, 2014. "On relations between DEA-risk models and stochastic dominance efficiency tests," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 13-35, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Y.M. Ermoliev & T.Y. Ermolieva & G.J. MacDonald & V.I. Norkin, 1998. "On the Design of Catastrophic Risk Portfolios," Working Papers ir98056, International Institute for Applied Systems Analysis.
    2. Ermoliev, Yuri M. & Ermolieva, Tatiana Y. & MacDonald, Gordon J. & Norkin, Vladimir I. & Amendola, Aniello, 2000. "A system approach to management of catastrophic risks," European Journal of Operational Research, Elsevier, vol. 122(2), pages 452-460, April.
    3. X. Qin & G. Huang, 2009. "An Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(4), pages 661-695, March.
    4. Dipankar Mondal & N. Selvaraju, 2022. "Convexity, two-fund separation and asset ranking in a mean-LPM portfolio selection framework," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 225-248, March.
    5. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    6. Briskorn, Dirk & Horbach, Andrei, 2009. "A Lagrangian approach for minimum cost tournaments," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 647, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    7. Nowak, Maciej, 2007. "Aspiration level approach in stochastic MCDM problems," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1626-1640, March.
    8. William B. Haskell & Wenjie Huang & Huifu Xu, 2018. "Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions," Papers 1805.06632, arXiv.org.
    9. Miller, Naomi & Ruszczynski, Andrzej, 2008. "Risk-adjusted probability measures in portfolio optimization with coherent measures of risk," European Journal of Operational Research, Elsevier, vol. 191(1), pages 193-206, November.
    10. Righi, Marcelo Brutti & Borenstein, Denis, 2018. "A simulation comparison of risk measures for portfolio optimization," Finance Research Letters, Elsevier, vol. 24(C), pages 105-112.
    11. Li, Jie & Huang, Huaxia & Xiao, Xiao, 2012. "The sovereign property of foreign reserve investment in China: A CVaR approach," Economic Modelling, Elsevier, vol. 29(5), pages 1524-1536.
    12. Alessandra Carleo & Francesco Cesarone & Andrea Gheno & Jacopo Maria Ricci, 2017. "Approximating exact expected utility via portfolio efficient frontiers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 115-143, November.
    13. Niu, Cuizhen & Wong, Wing-Keung & Xu, Qunfang, 2017. "Higher-Order Risk Measure and (Higher-Order) Stochastic Dominance," MPRA Paper 75948, University Library of Munich, Germany.
    14. Walter J. Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    15. Victor Lebreton, 2007. "Le trading algorithmique," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00332823, HAL.
    16. Li, Y.P. & Huang, G.H. & Zhang, N. & Nie, S.L., 2011. "An inexact-stochastic with recourse model for developing regional economic-ecological sustainability under uncertainty," Ecological Modelling, Elsevier, vol. 222(2), pages 370-379.
    17. Büther, Marcel, 2008. "Beam search for the elastic generalized assignment problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 634, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    18. Li, Y.P. & Huang, G.H. & Nie, S.L. & Chen, X., 2011. "A robust modeling approach for regional water management under multiple uncertainties," Agricultural Water Management, Elsevier, vol. 98(10), pages 1577-1588, August.
    19. T. Ermolieva & T. Filatova & Y. Ermoliev & M. Obersteiner & K. M. de Bruijn & A. Jeuken, 2017. "Flood Catastrophe Model for Designing Optimal Flood Insurance Program: Estimating Location‐Specific Premiums in the Netherlands," Risk Analysis, John Wiley & Sons, vol. 37(1), pages 82-98, January.
    20. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2016. "Coherent Pricing," INDEM - Working Paper Business Economic Series 22932, Instituto para el Desarrollo Empresarial (INDEM).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:216:y:2012:i:2:p:376-385. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.