Kernel minimum divergence portfolios

Chamakh, Linda and Szabo, Zoltan ORCID: 0000-0001-6183-7603 (2021) Kernel minimum divergence portfolios. . arXiv. (Submitted)

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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.

Item Type:	Monograph (Working Paper)
Official URL:	https://arxiv.org/list/stat/recent
Additional Information:	© 2021 The Authors
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	01 Aug 2022 09:27
Last Modified:	17 Oct 2024 16:25
URI:	http://eprints.lse.ac.uk/id/eprint/115723

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