模糊期望值及其在財金預測之應用

Abstract

由於電腦革命的成功，在短暫的幾年之間，更加速了經濟的成長，而金融的投資分析，是社會經濟發展的原動力，因此研究這方向的財務數學也相對的提高了專家、學者的研究熱潮。就以股票、匯率市場來說，如果能比别人早一步掌握行情走勢，就能獲得較高的利潤。但影響股價、匯率波動的因素很多，尤其是在複雜多變及不確定性的資訊下。因此；如何進行更精確的趨勢分析與預測，是本文研究的主題。由於，傳統的期望值是二元的邏輯思考(非1即0)，比較無法符合多變與不確定的財金問題，因此本文考慮以模糊統計方法，以模糊期望值的方法來作趨勢分析與預測，期望能對複雜多變的財金體系提共一套更精確合理的投資分析方法，可以提供投資者更多的訊息，做出明確的抉擇。最後；以我國集中市場加權股票指數、台幣對美元匯率及台積電股價為例，做一實例上的詳細探討。

Based on computer revolutionary coming off, economics grows fast in previous several years, then the investment analyze of finance is the impetus of development of society economic. Therefore, many experts and scholars are interested in the research of financial mathematics. Taking stock market and exchange market for example, if you can predict the future trend of market, you obtain more profit. However, there are many factors that act on stock prices and exchange rate. Especially, the market information is complicated and incomplete. How to go along accurate trend analysis and divination is the important point of the text research.\r\nBecause traditional expectation value is dibasic logic thought (either 1 or 0), that can’t conform to the highly changeable and uncertain finance problems. For this reason, in this research we propose an integrated procedure for fuzzy expectation value modeling and forecasting through fuzzy relation equations. We apply this technique to construct a fuzzy expectation value model for Taiwan Weighted Stock Index and exchange rate and forecast future trend. We strongly believe that this model will be profound of meaning in forecasting future trend of financial market.

目錄\r\n1、前言………………………………………………………………………4\r\n2、模糊期望質之引進………………………………………………………6\r\n2.1 模糊統計分析……………………………………………………………6\r\n2.2 模糊時間數列之預測……………………………………………………7\r\n2.3相關的模糊預測指標……………………………………………………9\r\n2.4模糊期望值模式建構步驟與流程………………………………………12\r\n3. 有關模糊期望值的一些性質……………………………………………13\r\n4、實例探討…………………………………………………………………17\r\n4-1、利用模糊期望值預測我國股票加權指數、台幣對美元匯率………17\r\n4.1-1股票加權指數資料分析一 ……………………………………………17\r\n4.1-2股票加權指數模糊模式建構一………………………………………19\r\n4.1-3股票加權指數資料分析二……………………………………………26\r\n4.1-4股票加權指數模糊模式建構二………………………………………28\r\n4.2、利用模糊期望值預測台幣對美元匯率………………………………35\r\n4.2-1台幣對美元匯率資料分析……………………………………………35\r\n4.2-2台幣對美元匯率的模糊式建構………………………………………37\r\n4-3、台積電股價之模糊期望值……………………………………………45\r\n4.3-1台積電股價資料分析…………………………………………………45\r\n4.3-2台積電股價模糊模式建構……………………………………………47\r\n5、結論………………………………………………………………………56\r\n6、參考文獻…………………………………………………………………57