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Kernel minimum divergence portfolios

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  • Chamakh, Linda
  • Szabo, Zoltan

Abstract

Portfolio optimization is a key challenge in finance with the aim of creating portfolios matching the investors' preference. The target distribution approach relying on the Kullback-Leibler or the f-divergence represents one of the most effective forms of achieving this goal. In this paper, we propose to use kernel and optimal transport (KOT) based divergences to tackle the task, which relax the assumptions and the optimization constraints of the previous approaches. In case of the kernel-based maximum mean discrepancy (MMD) we (i) prove the analytic computability of the underlying mean embedding for various target distribution-kernel pairs, (ii) show that such analytic knowledge can lead to faster convergence of MMD estimators, and (iii) extend the results to the unbounded exponential kernel with minimax lower bounds. Numerical experiments demonstrate the improved performance of our KOT estimators both on synthetic and real-world examples.

Suggested Citation

  • Chamakh, Linda & Szabo, Zoltan, 2021. "Kernel minimum divergence portfolios," LSE Research Online Documents on Economics 115723, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:115723
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    File URL: http://eprints.lse.ac.uk/115723/
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    References listed on IDEAS

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    More about this item

    Keywords

    kernel methods; divergence measure; optimal transport; portfolio allocation; concentration;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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