本論文介紹傅利葉轉換於亞式選擇權評價上的應用探討，並藉由與其他評價方式比較，來凸顯此評價方法不須對標的價格做分配假設的評價優勢，以及藉由快速傅利葉所具有的快速演算優勢，來看對亞式選擇權評價的影響。

高解析法是訊號處理上處理離散訊號系統的重要方法，將之運用在有限二項組合及有限卜瓦松組合的參數解上，可以得到很好的結果。本篇論文除了將高解析法在有限二項組合及有限卜瓦松之運用作一探討外，並在有限二項組合的基礎上推論有限負二項組合在特殊情況下的解法。 / High-resolution inversion method is an important technique to solve discrete signal system problems. We can solve finite binomial mixtures and finite Poisson mixture problems with high-resolution inversion method. In thispaper, we shall provide and discuss how the high-resolution inversion method used in finite binomial mixtures and finite Poisson mixture problems.In addition,we shall also extend our methods to solve finite negative binomial mixture problems with some assumptions same as those for finitebinomial mixtures.

本文採用傅利葉轉換與小波轉換以探討非線性現象：長期相依的碎形結構與混沌現象。藉由傅利葉轉換與小波轉換兩種研究方法，所得到臺灣股票市場加權股價指數的實證結論如下：1.藉由傅利葉轉換所得到的H值為0.4632；藉由小波轉換所得到的H值為0.4750。這兩種研究方法皆顯示臺灣股票市場具有負的長期相依的碎形結構。2.藉由傅利葉轉換的研究方法，臺灣股票市場加權股價指數的頻譜由初始向下與寬的連續的頻帶所組成；臺灣股票市場加權股價指數的自我相關函數則隨著時間差距的增加而遞減。此顯示臺灣股票市場具有混沌現象。3.小波轉換可以檢測出臺灣股票市場加權股價指數的奇異之處，並且指出存有一能說明臺灣股票市場碎形結構的複雜性的機制。藉由以上的實證結論，可以得知臺灣股票市場具有反持續性的碎形結構，股票價格的變動來自於臺灣股票市場尺度上的自我相似性。即使如此，由於混沌不可預測性的本質，使得股票價格的預測似乎是不可能的。 / The Fourier transform and the wavelet transform are utilized in this research to explore the nonlinear phenomena: the fractal structure of long trem dependence and the phenomenon of chaos. 　　In terms of the two research methods of the Fourier transform and the wavelet transform, the empirical conclusions of the Taiwan stock exchange weighted stock index are derived as follows: 　　1. The $H$ value of the research method of the Fourier transform is 0.4632; the $H$ value of the research method of the wavelet transform is 0.4750. The two research methods show that the Taiwan stock market has a fractal structure of negative long term dependence. 　　2. In terms of the research method of the Fourier transform, the power spectrum of the Taiwan stock exchange weighted stock index consists of initially downward and wide continuous band of frequencies; the autocorrelation function of the Taiwan stock exchange weighted stock index decreases as the time lag increases. These observations show that there exists the phenomenon of chaos in the Taiwan stock market. 　　3. The wavelet transform can detect out the singularities of the Taiwan stock exchange weighted stock index and can point out the heirarchy that illustrates the complexity of the fractal sturcture in the Taiwan stock market. 　　By the above empirical conclusions, there exists the antipersistent fractal structure in the Taiwan stock market. The variations of stock prices result from the self-similarity of the scales of the Taiwan stock market. Even so, the prediction of stock prices seems very impossible as a result of the unpredictability of chaotic nature.