機器學習演算法於投資組合問題之應用

Abstract

投資組合問題 (Portfolio Selection Problem) 是金融領域中的重要議題，自馬可維茲 (Markowitz) 提出現代投資組合模型，學者們對投資組合問題進行了諸多研究，其中部分學者嘗試將機器學習運用於此問題上，本論文重點參考基因演算法、粒子群演算法與免疫演算法。為使研究結果更貼近現實，我們採用拔靴法 (Bootstrapping) 進行風險值計算，直接由歷史資料中獲得風險值，避免假設造成模型缺漏。本論文提出二種新方法：改良後的新免疫演算法與各演算法之間的結合。新免疫演算法能記住過去獲得的資訊達到再利用的目的，實驗結果顯示了此演算法優秀的獲利能力，以95%-VaR上限為20%為例，新免疫演算法之複利獲利率為15.4%，基因演算法與粒子群演算法分別為12.55%與11.99% ；基因與粒子群、免疫與粒子群演算法之間的結合，能讓結果更為穩定，以免疫為例，與粒子群演算法的結合，成功使免疫演算法的標準差 (deviation) 由5.11%降為3.34%。

Portfolio selection problem is an important issue in finance. Since Markowitz established the modern portfolio model, experts have kept working on solving the portfolio selection problem with several techniques. In order to solve the portfolio selection problem, some experts applied machine learning techniques to the problem. In this thesis, we apply genetic algorithm (GA), particle swarm algorithm (PSO) and immune algorithm (IA) to the portfolio selection problem, and using bootstrapping method to estimate the VaR from the historical data. In our approach, we first propose a modified immune algorithm (IA) to reuse the memory cells we got in earlier stages, so that more information can be utilized in the next stages. Our experimental results show that the modified IA, whose average return in Taiwan 50 market is 15.4%, can successfully obtain significantly higher return than genetic algorithm and particle swarm optimization. Second, we also propose a hybrid of IA and PSO, and a hybrid of GA and PSO. From our experiments, the hybrid modified IA-PSO maintains the high return while becoming more stable. The deviation of modified IA-PSO (3.34%) is lower than the deviation of modified IA (5.11%).