股票市場上如何分配資產使其達到最佳化報酬,一直是最被關注的議題,研究 上也有許多不同方法,像是由馮·紐曼 (Von Neumann) 和摩根斯坦 (Morgenstern) 提出 並被後人發展的預期效用理論 (expected utility theory),或是馬可維茲 (Markowitz) 提 出的平均數-變異數投資組合模型 (Mean-Variance portfolio model)。一般來說,尋找 最佳化投資策略,通常是以收盤價格去計算,卻忽略了每日股票擁有的最高及最低 價等訊息,故本文的目標是利用收盤價、最高價及最低價去建立模型,用此模型預 測隔日的最高價及最低價,再利用前述兩個決策方法找到最佳投資組合。

The aim of this study is to optimize the trading strategy based on interval time series. We use daily opening price, closing price, the highest price and the lowest price to construct the model. Then, use this model to predict the highest and lowest prices step by step. Assume that the closing price has an uniform distribution with the parameters of upper bound to be the estimated highest price and lower bound to be the estimated lowest price. Finally, the optimal portfolio weights are obtained by using expected utility theory and Mean-Variance portfolio model. In empirical study, we perform the optimization trad- ing strategies of above two decision making methods in three different periods by using the historical observations to estimate the parameters respectively. The results show that the uniform assumption for the closing price have higher profits than the traditional one.

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