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arXiv · 2512.05645

On the supremum of a quotient of power sums

Stefan Gerhold·Friedrich Hubalek
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Abstract

We define a function of two real vectors by a certain homogeneous quotient involving power sums, and show that its supremum grows asymptotically linearly w.r.t. the dimension. From this, we deduce a condition under which a parametric set of real matrices satisfies a set of polynomial positivity constraints. This characterization finds an application in mathematical finance, in a recent study on price impact models.

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Stefan Gerhold, Friedrich Hubalek. 2025-12-05. On the supremum of a quotient of power sums. https://arxiv.org/abs/2512.05645

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