指數追蹤在現今的交易市場中是相當重要的一門技術，而其中以技術指標的應用最為廣泛。技術指標即是以過去市場資料來預測未來股價趨勢的一門技術。然而在此篇文章中，我們透過控制問題的假設來處理指數追蹤：找出最佳化策略並提供證明。;Tracing index in the market is now a crucial and popular topic in finance. In practice, the technical analysis for forecasting the direction index based no the past market data is widely used. In this paper, we construct a model to trace an index based on the technique of the portfolio optimization problem through the linear quadratic regulator. We solve the optimal strategy using the dynamic programming and the corresponding HJB equation. The verification theorem is also provided. Furthermore, the sensitive analysis is illustrated through the numerical study. Finally, we examine the proposed strategy is by real data included S&P 500 and several individual stocks in the U.S.
