分位数曲面的渐近形状
On the asymptotic shape of quantile surfaces
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中文总结 AI 辅助
本文研究受控一维分布（对数正态随机变量线性组合）的分位数曲面渐近形状，证明左尾全局凹、右尾全局凸，并展示尺度与形状的渐近分离。
中文摘要 AI 辅助
本文关注分位数曲面的渐近形状，该曲面定义为由受控的一维分布在给定水平 $\alpha$ 下生成的分位数集合。具体而言，当该分布表现为对数正态随机变量的线性组合，且控制为正系数向量时，我们证明分位数曲面在左尾（$\alpha\to0$）全局凹，在右尾（$\alpha\to1$）全局凸。此外，这些曲面表现出尺度与形状的渐近分离。
英文摘要
This article is concerned with the asymptotic shape of quantile surfaces, defined as the set of quantiles at a given level $α$ 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 ($α\to0$) and globally convex in the right tail ($α\to1$). Moreover, these surfaces exhibit asymptotic separation of scale and shape.
发表机构
- Austrian Financial Market Authority（奥地利金融市场管理局）
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