AI 中文总结
研究凯尔知情交易模型中适应随机流动性和多资产的情况，通过变分公式从原对偶问题导出鞅，验证构造，将一般矩阵值情况简化为耦合矩阵FBSDE，还建立杜布 - 迈耶分解，给出主要均衡结果。
AI 中文摘要
我们开发了凯尔知情交易模型的变分公式，以适应随机流动性和多种交易资产。首先阐述主要均衡结果：在鞅对偶条件下，矩阵值鞅深度过程生成具有随机矩阵值价格影响的线性高斯均衡。我们从受因果最优传输启发的原对偶问题中导出此鞅，该问题表征内部人将私人信息注入价格的内生速度。一般而言，此问题仅允许局部鞅优化器，鞅对偶条件是优化器为真鞅的假设。我们将知情交易解释为私人信息的最优清算，并在标量和共同特征基情况下验证了构造。完全一般的矩阵值情况简化为耦合矩阵FBSDE，这是我们分离出的剩余障碍。在此过程中，我们为一般（不一定对称）矩阵值次鞅建立了一个独立有趣的杜布 - 迈耶分解。
英文摘要
We develop a variational formulation of Kyle's model of informed trading that accommodates stochastic liquidity and multiple traded assets. The main equilibrium result is stated first: under a martingale dual condition, a matrix-valued martingale depth process generates a linear-Gaussian equilibrium with stochastic matrix-valued price impact. We derive this martingale from a primal-dual problem, inspired by causal optimal transport, that characterizes the endogenous speed at which the insider injects private information into prices; in general, this problem admits only local martingale optimizers, and the martingale dual condition is the hypothesis that the optimizer is a true martingale. We interpret informed trading as the optimal liquidation of private information and verify the construction in the scalar and common-eigenbasis cases. The fully general matrix-valued case reduces to a coupled matrix FBSDE, which we isolate as the remaining obstruction. Along the way, we establish an independently interesting Doob-Meyer decomposition for general (not necessarily symmetric) matrix-valued submartingales.
Comments44 pages
