标题： 多期交易通过凸优化 显示英文标题

标题： Multi-Period Trading via Convex Optimization

摘要： 我们考虑一个多期交易的基本模型，该模型可用于评估交易策略的性能。 我们描述了一个单期优化的框架，在该框架中，每期的交易通过求解一个凸优化问题来确定，该问题在预期收益、风险、交易成本和持有成本（如做空资产的借款成本）之间进行权衡。 然后我们描述了该交易方法的多期版本，在该版本中，优化用于规划一系列交易，仅执行第一个交易，使用在选择交易时未知的未来数量的估计值。 单期方法可以追溯到马科维茨；多期方法可以追溯到模型预测控制。 我们的贡献是将单期和多期方法纳入一个简单的框架中，清晰地描述了其发展过程和所做的近似。 在本文中，我们没有涉及交易算法中的一个关键组件，即对未来数量的预测或预报。 我们在这篇文章中描述的方法可以被视为利用预测的好方法，无论这些预测是如何做出的。 我们还开发了一个配套的开源软件库，实现了本文中描述的许多想法和方法。 显示英文摘要

摘要： We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single-period method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper.