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On the asymptotic shape of quantile surfaces

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  • Florian Gach
  • Simon Hochgerner

Abstract

This article is concerned with the asymptotic shape of quantile surfaces, defined as the set of quantiles at a given level $\alpha$ generated by a controlled one-dimensional distribution. Specifically, when the distribution arises as a linear combination of log-normal random variables and the control is a vector of positive coefficients, we prove that quantile surfaces are globally concave in the left tail ($\alpha\to0$) and globally convex in the right tail ($\alpha\to1$). Moreover, these surfaces exhibit asymptotic separation of scale and shape.

Suggested Citation

  • Florian Gach & Simon Hochgerner, 2026. "On the asymptotic shape of quantile surfaces," Papers 2609.31345, arXiv.org, revised Oct 2026.
    • Handle: RePEc:arx:papers:2609.31345
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    File URL: https://arxiv.org/pdf/2609.31345
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    References listed on IDEAS

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    1. Danielsson, Jon & Jorgensen, Bjørn N. & Mandira, Sarma & Samorodnitsky, Gennady & Vries, C. G. de, 2005. "Subadditivity re–examined: the case for value-at-risk," LSE Research Online Documents on Economics 24668, London School of Economics and Political Science, LSE Library.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496, December.
    3. Stéphane Crépey & Noufel Frikha & Azar Louzi & Jonathan Spence, 2026. "Adaptive Multilevel Stochastic Approximation of the Value-at-Risk [Approximation stochastique adaptative à plusieurs niveaux de la valeur à risque]," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04670735, HAL.
    4. St'ephane Cr'epey & Noufel Frikha & Azar Louzi & Jonathan Spence, 2024. "Adaptive Multilevel Stochastic Approximation of the Value-at-Risk," Papers 2408.06531, arXiv.org, revised Apr 2026.
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