特殊马科维茨：收益与协方差联合正则化的热力学形式
Special Markowitz: Thermodynamic Formalism for the Joint Regularisation of Returns and Covariance
浏览论文内容
中文总结 AI 辅助
本文提出特殊马科维茨方法，利用热力学形式联合正则化收益与协方差，通过谱可靠性势和吉布斯权重保留可靠模式、松弛不可靠模式，并证明压力泛函的可加性。
中文摘要 AI 辅助
特殊马科维茨（Special Markowitz, SM）相对于参考状态（mu_ref, Sigma_ref）联合正则化收益和协方差。白化相对算子的每个特征方向都携带一个谱可靠性势Phi_k，该势由其估计质量推导而来。其吉布斯权重exp(-Phi_k)同时控制收益信号中保留的比例和协方差偏差中保留的比例。可靠模式（低Phi_k）被保留；不可靠模式（高Phi_k）松弛至参考状态。对数势坐标具有乘法组合律特征；斯坦损失被表征为与所得耦合兼容的唯一自由能密度（在自然类内）。SM压力泛函在模式间可加——这是特殊马科维茨的定义性属性。
英文摘要
Special Markowitz (SM) regularises returns and covariance jointly, relative to a reference state (mu_ref, Sigma_ref). Each eigendirection of the whitened relative operator carries a signed spectral potential Phi_k, with persistence factor psi_k = exp(-Phi_k) > 0. Positive potentials attenuate empirical deviations from the reference geometry, zero potential preserves them, and negative potentials amplify them. The persistence factor psi_k governs both the return signal and the covariance deviation: the regularised deviation from the reference is psi_k times the empirical deviation. The logarithmic potential coordinate is characterised by a multiplicative composition law on the multiplicative group of positive real numbers; the Stein loss is characterised as the unique free-energy density (within a natural class) compatible with the resulting coupling. The SM pressure functional is additive across modes the defining property of Special Markowitz.
发表机构
- studio entropica（Entropica 工作室）
机构由 AI 辅助整理，请以论文原文为准。
