Kernel Minimum Divergence Portfolios. (arXiv:2110.09516v1 [stat.ML])

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.



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