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Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach

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  • Roberto Baviera
  • Giulia Bianchi

Abstract

In this paper we consider the worst-case model risk approach described in Glasserman and Xu (2014). Portfolio selection with model risk can be a challenging operational research problem. In particular, it presents an additional optimisation compared to the classical one. We find the analytical solution for the optimal mean-variance portfolio selection in the worst-case scenario approach. In the minimum-variance case, we prove that the analytical solution is significantly different from the one found numerically by Glasserman and Xu (2014) and that model risk reduces to an estimation risk. A detailed numerical example is provided.

Suggested Citation

  • Roberto Baviera & Giulia Bianchi, 2019. "Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach," Papers 1902.06623, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1902.06623
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    References listed on IDEAS

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    1. Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 267-279, January.
    2. Penev, Spiridon & Shevchenko, Pavel V. & Wu, Wei, 2019. "The impact of model risk on dynamic portfolio selection under multi-period mean-standard-deviation criterion," European Journal of Operational Research, Elsevier, vol. 273(2), pages 772-784.
    3. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    4. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    5. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    8. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
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