Survey_PortfolioSelection

Online portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning, and data mining, etc. This article aims to provide a comprehensive survey and a structural understanding of published online portfolio selection techniques.

Contributor: Victor Xiao, Dustin Yu, Yanpeng Wang, John Zhou, Polo Li, Joanne Wu, Kevin Wang, Jason Ji (Random Order)

OUTLINE

Section 1 线上资产选择问题，及其领域纵览。

Section 2 将正式赋予线上资产选择问题的数学定义，并探讨几个重要的实际问题。

Section 3 主要介绍产业内的重点算法 -3.1 基准算法 -3.2 跟随赢家 -3.3 跟随败者 -3.4 规律套利 -3.5 荟萃学习

Section 4 探讨现有算法与资产增长理论的核心交易理念

Section 5 谈论几个领域内的重点问题

Section 6 总结与未来方向展望

Section I. Overview

 线上资产组合选择（OLPS)，是优化一组资产的财富分配和长期增长的解法问题，是一直以来量化金融和金融工程实践领域的核心。在探索这个问题的道路上，主要形成了两个学派: 其一，基于马科维茨和其所在金融界发展出的均值方差理论。其二，本质起源于信息论的资本增长理论。在资产管理行业中，众所周知的均值方差理论（Mean-Variance Theory）着重于单期（批量）投资组合选择，通过权衡投资组合的预期收益（即，均值）和风险（即，方差），在投资者的风险收益偏好下，构筑最优。另一方面，资本增长理论（Capital Growth Theory）侧重于多期或连续投资组合的选择，旨在最大化投资组合的预期增长率或预期对数收益。虽然这两种理论都解决了投资组合选择的任务，但是对于我们追求的迭代性的投资策略来说，后者更适用这种本质便是连续性决策问题的基本环境。

This is derivative work from literature review of a paper, intending to serve as main alpha for the research project developed under ETC Investment Group, Academy Division. The underlying logic and technique follows through with the abstract:

From an online machine learning perspective, we first formulate online portfolio selection as a sequential decision problem, and then survey a variety of state-of-the-art approaches, which are grouped into several major categories, including benchmarks, “Follow-the-Winner” approaches, “Follow-the-Loser” approaches, “Pattern-Matching” based approaches, and “Meta-Learning Algorithms”. In addition to the problem formulation and related algorithms, we also discuss the relationship of these algorithms with the Capital Growth theory in order to better understand the similarities and differences of their underlying trading ideas. This article aims to provide a timely and comprehensive survey for both machine learning and data mining researchers in academia and quantitative portfolio managers in the financial industry to help them understand the state-of-the-art and facilitate their research and practical applications. We also discuss some open issues and evaluate some emerging new trends for future research directions.

In recent years, machine learning has been applied to various applications in finance (Gy¨orfi et al., 2012), including On-line Portfolio Selection, which aims to sequentially allocate capital among a set of assets, such that the investment return can be maximized in the long run (Kelly, 1956). It has attracted increasing attention from both academia and industry, and several machine learning algorithms have been proposed (Li and Hoi, 2014), including traditional algorithms (Cover, 1991; Helmbold et al., 1998; Agarwal et al., 2006; Borodin et al., 2004; Gy¨orfi et al., 2006, 2008), and recent state-of-the-art online learning algorithms (Li et al., 2011, 2012, 2013, 2015). Unlike other application domains in machine learning where various open-source packages are available, very few open-source toolkits exist for on-line portfolio selection, primarily due to the confidential nature of financial industry. Consequently, it is difficult for researchers to evaluate new algorithms for comprehensive comparisons with existing ones.

I. 一些经典策略

1. 基准策略Benchmark: 是一种追求长期大盘或是获取大盘自筛选性收益形成的算法类型。这种策略的基本假设就是市场有效假说，且大盘长期向上。

   Ex:Buy and hold, Best Stock, Constant Rebalanced Portfolio

2. 跟随赢家Follow the Winner：如名所指，旨在不断追随大盘领先者以获取收益的方法。是一种将仓位配比由underperformed资产调至outperformed的资产，以保证长期持有赢家的策略。这种策略的基本假设，是赢者稳赢。

   Ex:Universal Portfolio, Exponential Gradient, Follow the Leader, Follow the Regularized Leader, Aggregate-Type Leader

3. 跟随败者Follow the Loser：这种策略的思路与上一策略相反，基本假设是现阶段的败者有机会反弹，并反超其他资产实现收益。如此，这种策略的特点是将outperformed的资产调至underperformed的资产中。

   Ex:Anti-correlation, Passive Aggressive Mean Reversion, Confidence Weighted Mean Reversion, Online Moving Average Reversion.

4. 规律套利Patterns Arbitrage：这种套利策略的基本假设与EMH相反，相信市场并非完全随机漫步，存在必然有迹可循的客观规律。如此，并非完全随机的市场时间序列就可以作为寻找规律的数据集。技术分析的根本思路，其实也与此类似。

5. 荟萃学习算法Meta Learning Algorithm： 在机器学习中，学习，一般指代对特定代价函数的优化，我们最大化贝叶斯模型的似然估计，最小化神经网络中的平均方差，或是最大化增强学习中的期望回报。荟萃学习，则是优化这种机器学习进程的策略。

   EX:Aggregating Algorithms，Fast Universalization, Online Gradient Updates, Follow the Leading History.

II. Problem Setting.