統計機器學習在最佳成長投資組合之應用

Abstract

最佳成長投資組合（GOP）是在任何時間範圍內都具有最大期望增長率的投資組合，隨著時間範圍的增加，這種投資組合肯定會勝過其他任何不同的投資策略。在本文中，我使用了非母數統計方法和統計機器學習工具來估計市場數據的分佈。此外，模擬了平穩型數據和非平穩型數據以表示市場數據，通過了解市場分佈，我建立了最佳成長投資組合。GOP的文獻綜述在第1節中、理論研究在第2節中介紹、方法將在第3節中簡要介紹且在第4節中做出模擬結果。

The growth-optimal portfolio (GOP) is a portfolio which has a maximal expected growth rate over any time horizon. As a consequence, this portfolio is certain to outperform any other significantly different strategy as the time horizon increases. In this thesis, I used nonparametric statistic and machine learning tools to estimate the distribtuion of market data. Also, simulated both stationary and nonstationary data to represent market data. Through understanding the distribution of market, I built up the growth-optimal portfolio. The literature reviewing of GOP are in section 1. The theoretical studieso are presented in section 2. Methodology will be briefly introduced in section 3. Simulation results are in section 4.