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Portfolios with nonlinear constraints and spin glasses

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  • Gábor, Adrienn
  • Kondor, I

Abstract

In a recent paper Galluccio, Bouchaud and Potters demonstrated that a certain portfolio problem with a nonlinear constraint maps exactly onto finding the ground states of a long-range spin glass, with the concomitant nonuniqueness and instability of the optimal portfolios. Here we put forward geometric arguments that lead to qualitatively similar conclusions, without recourse to the methods of spin glass theory, and give two more examples of portfolio problems with convex nonlinear constraints.

Suggested Citation

  • Gábor, Adrienn & Kondor, I, 1999. "Portfolios with nonlinear constraints and spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 222-228.
    • Handle: RePEc:eee:phsmap:v:274:y:1999:i:1:p:222-228
    DOI: 10.1016/S0378-4371(99)00387-8
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    Cited by:

    1. Imre Kondor & István Csabai & Gábor Papp & Enys Mones & Gábor Czimbalmos & Máté Sándor, 2014. "Strong random correlations in networks of heterogeneous agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 203-232, October.
    2. Papp, Gábor & Caccioli, Fabio & Kondor, Imre, 2019. "Bias-variance trade-off in portfolio optimization under expected shortfall with ℓ 2 regularization," LSE Research Online Documents on Economics 100294, London School of Economics and Political Science, LSE Library.
    3. Lisewski, Andreas Martin & Lichtarge, Olivier, 2010. "Untangling complex networks: Risk minimization in financial markets through accessible spin glass ground states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3250-3253.
    4. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    5. Varga-Haszonits, Istvan & Caccioli, Fabio & Kondor, Imre, 2016. "Replica approach to mean-variance portfolio optimization," LSE Research Online Documents on Economics 68955, London School of Economics and Political Science, LSE Library.
    6. M. Andrecut, 2013. "Spin Glasses and Nonlinear Constraints in Portfolio Optimization," Papers 1311.2511, arXiv.org.
    7. G'abor Papp & Fabio Caccioli & Imre Kondor, 2016. "Bias-variance trade-off in portfolio optimization under Expected Shortfall with $\ell_2$ regularization," Papers 1602.08297, arXiv.org, revised Jul 2018.
    8. Imre Kondor & G'abor Papp & Fabio Caccioli, 2016. "Analytic solution to variance optimization with no short-selling," Papers 1612.07067, arXiv.org, revised Jan 2017.

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