Optimal Order Execution Using Equilibrium Theory and Big Data

这位研究人员、他的合作者和他的学生试图建立数学模型，说明如何在短时间内以最佳方式买卖给定数量的股票。该项目的新颖性在于，将使用经济学文献中的数学和均衡理论来开发模型：(I)将股票价格动态内生为模型输出，以及(Ii)可以处理大数据问题，例如非常频繁地出现大量新的相关数据点。目前，从业者和学术界使用的所有交易执行模型都不是基于合理和长期存在的经济学原理，即股票价格应该由股票需求与可用股票供应相等来确定。从严格的数学角度出发，首先从严格的数学角度证明了由布朗运动和更一般的Levy过程控制的连续时间执行模型的平衡点的存在性。随后，研究者试图调查这些模型的唯一性和稳定性。人们怀疑唯一性失败了，这意味着一种精细化的需要：如何最佳地选择一种均衡？这种优化在数学金融中产生了一类新的问题，与分析中的变分理论有关。此外，均衡模型经过精心设计，在数学上易于处理的同时，可以处理大数据代表的许多实际问题。需要解决的主要大数据问题是新的相关数据的不断到来，这迫使模型实施成为一种在线算法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The investigator, his collaborators, and his students seek to develop mathematical models for how to optimally buy or sell a given quantity of stocks over a short time interval. The project's novelty lies in the fact that both mathematics and equilibrium theory from the economics literature will be used to develop models which: (i) endogenize stock price dynamics as model output, and (ii) can deal with Big Data issues such as the very frequent arrival of massive amounts of new relevant data points. Currently, all trade execution models used by both practitioners and academics are not based on the sound and long standing economic principle which says that the stock price should be determined by equating stock demand with available stock supply. The goal is to build mathematically tractable models based on equilibrium theory which can deal with several Big Data issues.From a rigorous mathematical perspective, the investigator first seeks to prove existence of equilibria in continuous-time execution models governed by Brownian motions and more generally governed by Levy processes. Subsequently, the investigator seeks to investigate uniqueness and stability of these models. It is suspected that uniqueness fails which implies a refinement need: How to optimally choose an equilibrium? This optimization produces a new class of problems in mathematical finance related to the theory of calculus of variations from analysis. Furthermore, the equilibrium models are carefully designed such that while being mathematically tractable, the models can deal with many of the practical issues Big Data represent. The main Big Data issue to be addressed is the continuous arrival of new relevant data which forces the model implementation to be as an online algorithm.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.