Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 67, 2018 - Issue 2
245
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Robust mean variance optimization problem under Rényi divergence information

, &
Pages 287-307 | Received 27 Apr 2017, Accepted 13 Oct 2017, Published online: 27 Oct 2017

References

  • Markowitz HM. Portfolio selection. J. Finance. 1952;7:77–91.
  • Best MJ, Grauer RR. On the sensitivity of mean-variance efficient portfolios to changes in asset means: some analytical and computational results. Rev Financ Stud. 1991;4:315–342.
  • Chopra VK, Ziemba WT. The effects of errors in means, variances, and covariances on optimal portfolio choice. J Portfolio Manage. 1993;19:6–11.
  • DeMiguel V, Garlappi L, Nogales FJ, Uppal R. Generalized approach to portfolio optimization: improving performance by constraining portfolio norms. Manage Sci. 2009;22:1915–1953.
  • Ben-Tal A, El Ghaoui L, Nemirovski A. Robust optimization. Princeton (NJ): Princeton University Press; 2009.
  • Bertsimas D, Brown DB, Caramanis C. Theory and application of robust optimization. SIAM Rev. 2011;53:464–501.
  • Bertsimas D, Sim M. The price of robustness. Oper Res. 2004;52:35–53.
  • Fabozzi FJ, Huang D, Zhou G. Robust portfolios: contributions from operations research and finance. Ann Oper Res. 2010;176:191–220.
  • Goldfarb D, Iyengar G. Robust portfolio selection problems. Math Oper Res. 2003;28:1–38.
  • Tütüncü RH, Koenig M. Robust asset allocation. Ann Oper Res. 2004;132:157–187.
  • Pınar MÇ. On robust mean-variance portfolios. Optimization. 2016;65:1–10.
  • Fabozzi FJ, Kolm PN, Pachamanova DA, Focardi SM. Robust portfolio optimization and management. New York (NY): Wiley; 2007.
  • Garlappi L, Uppal R, Wang T. Portfolio selection with parameter and model uncertainty: a multi-prior approach. Rev Financ Stud. 2004;20:41–81.
  • Lu Z. Robust portfolio selection based on a joint ellipsoidal uncertainty set. Optim Methods Softw. 2011;26:89–104.
  • Zhu L, Coleman TF, Li Y. Min--max robust and CVaR robust mean-variance portfolios. J Risk. 2009;11:1–31.
  • Zymler S, Rustem B, Kuhn D. Robust portfolio optimization with derivative insurance guarantees. Eur J Oper Res. 2011;210:410–424.
  • Kullback BS, Leibler RA. On information and sufficiency. Ann Math Stat. 1951;22:79–86.
  • Rényi A. On measures of entropy and information. In: Neyman J, editor. Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability. Vol. I. Berkeley (CA): University of California Press; 1961. p. 547–561.
  • Broniatowski M, Toma A, Vajda I. Decomposable pseudodistances and applications in statistical estimation. J Stat Plan Infer. 2012;142:2574–2585.
  • Broniatowski M, Vajda I. Several applications of divergence criteria in continuous families. Kybernetica. 2012;48:600–636.
  • Pardo L. Statistical inference based on divergence measures. New York (NY): Chapman & Hall/CRC; 2006.
  • Ahonen SJ, Arumilli M, Lohi H. Maximum entropy principle with general deviation measures. Math Oper Res. 2009;34:445–467.
  • Atar R, Chowdhary K, Dupuis P. Robust bounds on risk-sensitive functionals via Rényi divergence. SIAM J Uncertainty Quant. 2015;3:18–33.
  • Ben-Tal A, Den Hertog D, Waegenaere AD, Melenberg B, Rennen G. Robust solutions of optimization problem Affected by uncertain probabilities. Manage Sci. 2013;59:341–357.
  • Gorissen BL, Blanc H, Den Hertog D, Ben-Tal A. Technical note-deriving robust and globalized robust solutions of uncertain linear programs with general convex uncertainty sets. Oper Res. 2012;62:672–679.
  • Hu Z, Hong L. Kullback-Leibler divergence constrained distributionally robust optimization. Available at Optimization Online. 2012.
  • Yanıkoğlu \.{I}, Den Hertog D. Safe approximation of ambiguous chance constraints using historical data. Informs J Comput. 2013;25:666–681.
  • Calafiore GC. Ambiguous risk measures and optimal robust portfolio. SIAM J Optim. 2007;18:853–877.
  • Yam SCP, Yang HL, Yuen FL. Optimal asset allocation: risk and information uncertainty. Eur J Oper Res. 2014;251:554–561.
  • Erven TV, Harremos P. Rényi divergence and Kullback-Leibler divergence. IEEE Trans Inform Theory. 2012;60:3797–3820.
  • Toma A, Leoni-Aubin S. Portfolio selection using minimum pseudodistance estimators. Econ Comput Econ Cybern. 2013;47:97–112.
  • Toma A, Leoni-Aubin S. Robust portfolio optimization using pseudodistances. PLoS ONE. 2015;10:1–26.
  • Sharpe WF. Capital asset prices: a theory of market equilibrium under conditions of risk. J Finance. 1964;19:425–442.
  • Bernstein DS. Matrix mathematics: theory, facts, and formulas. Princeton (NJ): Princeton University Press; 2009.

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.