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Multiperiod Mean-Variance Optimization with Intertemporal Restrictions

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Abstract

We investigate mean-variance optimization problems that arise in portfolio selection. Restrictions on intermediate expected values or variances of the portfolio are considered. Some explicit procedures for obtaining the solution are presented. The main advantage of this technique is that it is possible to control the intermediate behavior of a portfolio’s return or variance. Some examples illustrating these situations are presented.

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References

  1. Campbell, J.Y., Lo, A.W., MacKinlay, A.C.: The Econometrics of Financial Markets. Princeton University Press, Princeton (1997)

    MATH  Google Scholar 

  2. Elton, E.J., Gruber, M.J.: Modern Portfolio Theory and Investment Analysis. Wiley, New York (1995)

    Google Scholar 

  3. Jorion, P.: Portfolio optimization in practice. Financ. Analysts J. 1, 68–74 (1992)

    Article  Google Scholar 

  4. Steinbach, M.: Markowitz revisited: mean-variance models in financial portfolio analysis. SIAM Rev. 43, 31–85 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Roll, R.: A mean/variance analysis of tracking error. J. Portfolio Manag. 18, 13–22 (1992)

    Article  Google Scholar 

  6. Rudolf, M., Wolter, H.J., Zimmermann, H.: A linear model for tracking error minimization. J. Bank. Financ. 23, 85–103 (1999)

    Article  Google Scholar 

  7. Hanza, F., Janssen, J.: The mean-semivariances approach to realistic portfolio optimization subject to transactions costs. Appl. Stoch. Models Data Anal. 14, 275–283 (1998)

    Article  Google Scholar 

  8. David, A.: Fluctuating confidence in stock markets: implication for returns and volatility. J. Financ. Quant. Anal. 32, 427–462 (1997)

    Article  Google Scholar 

  9. David, A., Veronesi, P.: Option prices with uncertain fundamentals: theory and evidence of the dynamics of implied volatilities. Federal Reserve Board, Working Paper (1999)

  10. Rustem, B., Becker, R.G., Marty, W.: Robust min-max portfolio strategies for rival forecast and risk scenarios. J. Econ. Dyn. Control 24, 1591–1621 (1995)

    Article  MathSciNet  Google Scholar 

  11. Howe, M.A., Rustem, B.: A robust hedging algorithm. J. Econ. Dyn. Control 21, 1065–1092 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  12. Howe, M.A., Rustem, B., Selby, M.J.P.: Multiperiod minimax hedging strategies. Eur. J. Oper. Res. 93, 185–204 (1996)

    Article  MATH  Google Scholar 

  13. Costa, O.L.V., Paiva, A.C.: Robust portfolio selection using linear matrix inequalities. J. Econ. Dyn. Control 26, 889–909 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Costa, O.L.V., Nabholz, R.B.: A linear matrix inequalities approach to robust mean semivariance portfolio optimization. In: Kontoghiorghes, E.J., Rustem, B., Siokos, S. (eds.) Computational Methods in Decision-Making, Economics and Finance. Applied Optimization Series, vol. 74, pp. 87–105. Kluwer Academic, New York (2002)

    Google Scholar 

  15. Zenios, S.A.: Financial Optimization. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  16. Duarte, A.M. Jr.: Fast computation of efficient portfolios. J. Risk 4, 71–94 (1999)

    Google Scholar 

  17. Chen, S., Li, X., Zhou, X.: Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim. 36, 1685–1702 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhou, X., Li, D.: Continuous-time mean-variance portfolio selection: a stochastic LQ framework. Appl. Math. Optim. 42, 19–33 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zhou, X., Yin, G.: Markowitz’s mean-variance portfolio selection with regime switching: a continuous-time model. SIAM J. Control Optim. 42, 1466–1482 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  20. Yin, G., Zhou, X.: Markowitz’s mean-variance portfolio selection with regime switching: from discrete-time models to their continuous-time limits. IEEE Trans. Autom. Control 49, 349–360 (2004)

    Article  MathSciNet  Google Scholar 

  21. Li, D., Ng, W.-L.: Optimal dynamic portfolio selection: multiperiod mean-variance formulation. Math. Financ. 10, 387–406 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. Leippold, M., Trojani, F., Vanini, P.: A geometric approach to multiperiod mean variance optimization of assets and liabilities. J. Econ. Dyn. Control 28, 1079–1113 (2004)

    Article  MathSciNet  Google Scholar 

  23. Zhu, S.-S., Li, D., Wang, S.-Y.: Risk control over bankruptcy in dynamic portfolio selection: a generalized mean-variance formulation. IEEE Trans. Autom. Control 49, 447–457 (2004)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Departamento de Engenharia de Telecomunicações e Controle, Escola Politécnica da Universidade de São Paulo, Sao Paulo, SP, Brazil

    O. L. V. Costa & R. B. Nabholz

Authors
  1. O. L. V. Costa
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  2. R. B. Nabholz
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Corresponding author

Correspondence to O. L. V. Costa.

Additional information

Communicated by C.T. Leondes.

The first author received financial support from CNPq (Brazilian National Research Council) Grants 472920/03-0 and 304866/03-2, FAPESP (Research Council of the State of São Paulo) Grant 03/06736-7, PRONEX Grant 015/98, and IM-AGIMB.

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Costa, O.L.V., Nabholz, R.B. Multiperiod Mean-Variance Optimization with Intertemporal Restrictions. J Optim Theory Appl 134, 257–274 (2007). https://doi.org/10.1007/s10957-007-9233-x

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  • DOI: https://doi.org/10.1007/s10957-007-9233-x

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