论文标题
通过Monge-Kantorovich双重性来通报交易的统一方法
A unified approach to informed trading via Monge-Kantorovich duality
论文作者
论文摘要
我们使用Monge-Kantorovich二元性和向后随机部分微分方程解决了广义的Kyle模型类型问题。 首先，我们表明，具有动态信息的广义凯尔模型可以重铸为带有分布约束的终端优化问题。因此，不平等尺寸的空间之间的最佳运输理论是自然工具。 其次，使用Kantorovich的潜力和运输地图确定了做市商的定价规则和针对知情交易者问题的最佳标准。 最后，我们通过从做市商的角度分析过滤问题来完全表征最佳策略。在这种情况下，Kushner-Zakai滤波SPDE产生了一个有趣的后退随机部分微分方程，该方程的度量值值来自测量的最佳耦合。
We solve a generalized Kyle model type problem using Monge-Kantorovich duality and backward stochastic partial differential equations. First, we show that the the generalized Kyle model with dynamic information can be recast into a terminal optimization problem with distributional constraints. Therefore, the theory of optimal transport between spaces of unequal dimension comes as a natural tool. Second, the pricing rule of the market maker and an optimality criterion for the problem of the informed trader are established using the Kantorovich potentials and transport maps. Finally, we completely characterize the optimal strategies by analyzing the filtering problem from the market maker's point of view. In this context, the Kushner-Zakai filtering SPDE yields to an interesting backward stochastic partial differential equation whose measure-valued terminal condition comes from the optimal coupling of measures.
