发表机构
Charles University（查理大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究异质波动率扩散模型的聚合方法，提出局部准则结合漂移信息与高斯冲击传输，并给出专家优先与候选优先投影的性质及金融应用。
AI 中文摘要
我们研究如何组合在漂移和协方差上存在分歧的扩散模型。候选优先的相对熵最小化给出几何池化，而专家优先的最小化给出与加权对数财富相关的算术混合。不同的二次变差可能使路径空间熵为无穷大，且算术混合不必是马尔可夫扩散。因此，我们指定一个局部准则，结合漂移信息（由第二个参数的协方差归一化）与固定状态度量下高斯冲击之间的二次传输。一个高斯恒等式和欧拉收敛估计证明了该选定准则的合理性。专家优先投影具有后验均值漂移和漂移离散度的逆协方差惩罚；在一维情形下，该惩罚增加波动率。对于具有共同均值回归速率的奥恩斯坦-乌伦贝克专家，系数正则性在共同波动率下于整个时间区间成立，在异质波动率下于初始时间之外成立。候选优先问题具有哈密顿-雅可比-贝尔曼刻画。其矩阵协方差选择器通过同余归约为Bures-Wasserstein重心。条件$H+\lambda M\succ0$，其中$H$为值函数的Hessian矩阵，$M$为状态度量，对于无约束局部协方差问题的有限性是尖锐的；紧约束使该问题保持有限。协方差分歧预算解释了惩罚参数。线性二次、精确转移和金融实例区分了动态波动率降低、漂移离散度膨胀和鞅限制。
英文摘要
We study how to combine diffusion models that disagree about drift and covariance. Candidate-first relative-entropy minimization gives geometric pooling, whereas expert-first minimization gives the arithmetic mixture associated with weighted logarithmic wealth. Different quadratic variations can make path-space entropy infinite, and the arithmetic mixture need not be a Markov diffusion. We therefore specify a local criterion combining drift information, normalized by the second argument's covariance, with quadratic transport between Gaussian shocks in a fixed state metric. A Gaussian identity and an Euler convergence estimate justify this chosen criterion. The expert-first projection has posterior-mean drift and an inverse-covariance penalty for drift dispersion; in one dimension this penalty increases volatility. For Ornstein--Uhlenbeck experts with a common mean-reversion rate, coefficient regularity holds on the full horizon for common volatility and away from the initial time for heterogeneous volatilities. The candidate-first problem has a Hamilton--Jacobi--Bellman characterization. Its matrix covariance selector reduces by congruence to a Bures--Wasserstein barycenter. The condition $H+λM\succ0$, with value Hessian $H$ and state metric $M$, is sharp for finiteness of the unrestricted local covariance problem; compact constraints keep that problem finite. A covariance-disagreement budget interprets the penalty parameter. Linear--quadratic, exact-transition, and financial examples distinguish dynamic volatility reduction, drift-dispersion inflation, and martingale restrictions.
