Generalization of Affine Feedback Stock Trading Results to Include Stop-Loss Orders

A class of recursive optimal stopping problems with applications to stock trading

In this paper we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multi-dimensional Markovian setting we show that the problem is well posed, in the sense that the value is indeed the unique solution to a fixed point problem in a suitable space of continuous functions, and an optimal stopping time exists. We then apply our class of problems to a model for stock trading in two different market venues and we determine the optimal stopping rule in that case.

The Impact of Execution Delay on Kelly-Based Stock Trading: High-Frequency Versus Buy and Hold

Stock trading based on Kelly's celebrated Expected Logarithmic Growth (ELG) criterion, a well-known prescription for optimal resource allocation, has received considerable attention in the literature. Using ELG as the performance metric, we compare the impact of trade execution delay on the relative performance of high-frequency trading versus buy and hold. While it is intuitively obvious and straightforward to prove that in the presence of sufficiently high transaction costs, buy and hold is the better strategy, is it possible that with no transaction costs, buy and hold can still be the bett…

On Drawdown-Modulated Feedback Control in Stock Trading

Control of drawdown, that is, the control of the drops in wealth over time from peaks to subsequent lows, is of great concern from a risk management perspective. With this motivation in mind, the focal point of this paper is to address the drawdown issue in a stock trading context. Although our analysis can be carried out without reference to control theory, to make the work accessible to this community, we use the language of feedback systems. The takeoff point for the results to follow, which we call the Drawdown Modulation Lemma, characterizes any investment which guarantees that the percen…

几何布朗运动下往返配对交易的最优策略

Optimal Strategies for Round-Trip Pairs Trading Under Geometric Brownian Motions

本文研究几何布朗运动假设下含固定交易成本的最大化收益配对交易策略，通过求解HJB方程得到阈值曲线刻画多、平、空初始状态下的往返开平仓最优策略。

基于强化学习的股票篮子清算最小缺口策略

Minimal Shortfall Strategies for Liquidation of a Basket of Stocks using Reinforcement Learning

针对机构投资者面临的大量高度相关股票清算难题，提出基于随机最优控制的强化学习新方法，解决传统方法的维度诅咒问题，最小化执行缺口，证明策略收敛性并基于日内数据实现算法。

各种机器学习模型的高频交易效应分析

Analysis of frequent trading effects of various machine learning models

本研究开发了一种基于神经网络的高频交易算法，并比较了交叉熵损失函数与拟牛顿算法结合、FCNN模型和向量机三种数学模型的性能，旨在为投资者提供更准确可靠的股票交易策略。