配對交易是華爾街經常使用的交易策略，經常被基金公司、避險基金公司或投資 銀行所採用。傳統文獻探討配對交易主要有三種方法，分別是距離法、協整性法 及隨機價差法，本文之最佳化交易策略主要是建構在隨機價差法上。先進行標的 資產的研究，接著利用隨機價差描繪配對交易的隨機控制問題，加入交易成本的 設定，最後由數值方法求出 Hamilton–Jacobi–Bellman (HJB)的數值解。

Spread trading is a popular short-term Wall Street trading strategy, in practice, is still used by many hedge funds and investment banks. There are three methods to study spread trading in the literature: the distance method, the cointegration method and the stochastic spread method. This paper build a model based on stochastic spread method. First, we focus on pair trading target selection. Second, we build a model to describe optimal stochastic control problem for pair trading trader. We add a transaction cost in the model. Finally, we solve the Hamilton–Jacobi–Bellman (HJB) by numerical.

第一章、 緒論-----------------------------------------------------5
第一節、研究背景與動機------------------------------------5
第二節、研究目標------------------------------------------5
第三節、研究架構------------------------------------------6
第二章、 標的商品分析---------------------------------------------7
第一節、永豐台灣股價指數 ETF 初步策略與結果----------------7
第二節、國際黃金現貨與白銀現貨初步策略與結果--------------17
第三節、本章小結------------------------------------------21
第三章、文獻回顧--------------------------------------------------22
第四章、最佳化模型建構--------------------------------------------24
第一節、無交易成本隨機控制模型----------------------------24
第二節、有交易成本隨機控制模型----------------------------27
第五章、研究方法--------------------------------------------------33
第一節、標的資產分析--------------------------------------33
第二節、參數估計------------------------------------------33
第三節、有限差分解 PDE-------------------------------------35
第六章、實證結果---------------------------------------------------37
第一節、標的資產分析---------------------------------------37
第二節、參數估計-------------------------------------------39
第三節、有限差分解 PDE-------------------------------------40
第四節、交易結果-------------------------------------------45
第七章、結論-------------------------------------------------------52
第八章、參考文獻---------------------------------------------------53
第九章、附錄-------------------------------------------------------56

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