跳至正文
返回文库全部文档

Ornstein–Uhlenbeck价格下的多资产执行与统计套利

文章 arXiv papers · 作者: Philippe Bergault et al.
阅读原文

总结

本文研究价格遵循多元Ornstein–Uhlenbeck动态时如何执行多种资产的大额订单。交易者的目标被设定为最大化盈亏的预期指数效用，因此执行决策考虑的是投资组合层面的风险，而非将每种资产孤立处理。

作者利用随机最优控制，将多维 Hamilton–Jacobi–Bellman 方程化简为常微分方程，其中包括矩阵 Riccati 方程。他们利用最优控制的界限推导该方程解的存在性和唯一性，并证明了所提解满足验证定理。外汇和股票市场数据示例展示了该方法及其对执行和统计套利的意义。论文摘要未提供具体数值结果或实现细节，因此说明了模型的理论基础和应用领域，但信息不足以评估其实盘交易表现。

核心观点

  • 该模型在价格遵循多元Ornstein–Uhlenbeck动态时优化跨资产组合的执行。
  • 优化目标是盈亏的预期指数效用。
  • 随机控制将问题化简为常微分方程，其中包括矩阵Riccati方程。
  • 最优控制界限支持Riccati方程解的存在性和唯一性结论。
  • 外汇和股票市场示例将该框架与执行及统计套利联系起来。

标签

多资产交易执行套利外汇股票
全文
# Multi-asset optimal execution and statistical arbitrage strategies under Ornstein-Uhlenbeck dynamics


# Multi-asset optimal execution and statistical arbitrage strategies under Ornstein-Uhlenbeck dynamics









In recent years, academics, regulators, and market practitioners have increasingly addressed liquidity issues. Amongst the numerous problems addressed, the optimal execution of large orders is probably the one that has attracted the most research works, mainly in the case of single-asset portfolios. In practice, however, optimal execution problems often involve large portfolios comprising numerous assets, and models should consequently account for risks at the portfolio level. In this paper, we address multi-asset optimal execution in a model where prices have multivariate Ornstein-Uhlenbeck dynamics and where the agent maximizes the expected (exponential) utility of her PnL. We use the tools of stochastic optimal control and simplify the initial multidimensional Hamilton-Jacobi-Bellman equation into a system of ordinary differential equations (ODEs) involving a Matrix Riccati ODE for which classical existence theorems do not apply. By using \textit{a priori} estimates obtained thanks to optimal control tools, we nevertheless prove an existence and uniqueness result for the latter ODE, and then deduce a verification theorem that provides a rigorous solution to the execution problem. Using examples based on data from the foreign exchange and stock markets, we eventually illustrate our results and discuss their implications for both optimal execution and statistical arbitrage.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。