為了瞭解影響演化性神經網路（ENT）預測表現的四項重要的機制：輸入資料性質、訓練樣本大小、網路搜尋密度以及控制模型複雜度，進而找出能使ENT充分發揮效果的組合。在本論文中首先設計ENT在模擬資料上的實驗，探討上述四項機制個別對預測表現的影響，再依照實驗結果的建議，設計能讓ENT發揮功效的組合，並以實際金融高頻率資料：香港恆生指數在一九九八年十二月報酬率為標的，探討模擬資料的結果在實際金融資料需要調整的部份。實驗結果顯示，當輸入資料經過線性過濾後，搭配大樣本訓練、高搜尋強度與適當地模型複雜度控制，會是能讓神經網路提高預測能力的組合。在實際金融資料的實驗當中同時發現，資料中偶而出現特別高或特別低的變化，會對ENT的預測表現有相當程度的影響。 / In this thesis, Evolutionary Neural Trees (ENTs) are applied to forecast the artificial data generated by financial and chaos models — iid random, linear process (Auto Regressive-Moving Average；ARMA), nonlinear processes (AutoRegressive Conditional Heteroskedasticity；ARCH, General AutoRegressive Conditional Heteroskedasticity；GARCH, Bilinear), mixed linear and nonlinear process (AR and GARCH). Experiments of the artificial data were conducted to understand the characteristics of ENTs mechanism. – data pre-processing procedures, search intensity, sample size and complexity regularization. From the experiment results of artificial data, the combination of pure linear or nonlinear time series, large sample size, intensive search and simple neural trees are suggested for the parameters setting of ENTs. And for the sake of computational burden, we have a trade-off between search intensity and sample size. Ten experiments are designed for ENTs modeling on the high-frequency stock returns of Heng Sheng stock index on December, 1998, in order to have an efficient combination of the factors of ENTs. The results show that ENTs would perform more efficiently if data are pre-processed by a linear filter, for ENTs will concentrate on searching in the space of nonlinear signals. Also, as is well demonstrated in this study, the infrequent bursts (outliers) appearing in the data set can be very disturbing for the ENTs modeling.

本研究中，我們計算OGA演化投資策略在五類時間數列模型上之表現，這五類模型分別是線性模型、雙線性模型、自迴歸條件異質變異數模型、門檻模型以及混沌模型。我們選擇獲勝機率、累積報酬率、夏普比例以及幸運係數做為評斷表現之準則，並分別推導出其漸近統計檢定。有別於一般計算智慧在財務工程上之應用，利用蒙地卡羅模擬法，研究中將對各表現準則提出嚴格之統計檢定結果。同時在實証研究中，我們考慮歐元兌美元及美元兌日圓的tick-by-tick匯率資料。故本研究主要的重點之一，乃是對於OGA演化投資策略，於這些模擬及實証資料上的有效性應用，作了深入且廣泛的探討。 / In this study, the performance of ordinary GA-based trading strategies are evaluated under five classes of time series model, namely, linear ARMA model, bilinear model, ARCH model, threshold model and chaotic model. The performance criteria employed are the winning probability, accumulated returns, Sharpe ratio and luck coefficient. We then provide the asymptotic statistical tests for these criteria. Unlike many existing applications of computational intelligence in financial engineering, for each performance criterion, we provide a rigorous statistical results based on Monte Carlo simulation. In the empirical study, two tick-by-tick foreign exchange rates are also considered, namely, EUR/USD and USD/JPY. As a result, this study provides us with a thorough understanding about the effectiveness of ordinary GA for evolving trading strategies under these artificial and natural time series data.

Black-Scholes選擇權定價模型是各種選擇定價的開山始祖，無論在理論或實務上均獲致許多的便利及好評，美中不足的是，這種既定模型下結構化參數的估計問題，在真實體系的結構訊息未知或是不明朗時，或是模式錯誤，亦或政治結構或金融環境不知時，該模型在實證資料的評價上會面臨價格偏誤的窘境。是故，許多的數值演算法（numerical algorithms）便因應而生，這些方法一則源於對此基本模型的修正，一則是屬於逼近的數值解。 評價選擇權的方法雖不一而足，然所有的這些理論或模型可分為二大類即模型驅動的理論（model-drive approach）及資料驅動的理論（data-driven approach）。前者是建構在許多重要的假設，當這些假設成立時，則選擇權的價格可用如Black-Scholes偏微分方程來表示，而後再用數值解法求算出，許多的數值方法即屬於此類的範疇；而資料驅動的理論（data-driven approach），其理論的特色是它的有效性（validity）不像前者是依其假設，職是之故，他在處理現實世界的財務資料時更顯見其具有極大的彈性。這些以計算智慧（computation intelligence）為主的財務計量方法，如人工神經網路（ANNs），遺傳演算法（GAs），遺傳規劃（GP）已在財務工程（financial engineering）領域上萌芽，並有日趨蓬勃的態勢，而將機器學習技術（machine learning techniques）應用在衍生性商品的定價，應是目前財務應用上最複雜及困難，亦是最富挑戰性的問題。 本文除了對現有文獻的整理評析外，在人工神經網路方面，除用於S&P 500的實證外，並用於台灣剛推行不久的認購構證評價之實證研究；而遺傳規劃在計算智慧發展的領域中，算是較年輕的一員，但發展卻相當的快速，雖目前在經濟及財務上已有一些文獻，但就目前所知的二篇文獻選擇權定價理論的文獻中，仍是試圖學習Black-Scholes選擇權定價模型，而本文則提出修正模型，使之成為完全以資料驅動的模型，應用於S&P 500實證，亦證實可行。最後，本文結合計算智慧中的遺傳演算法（ genetic algorithms）及數學上的加權殘差法（weight-residual method）來建構一條除二項式定價模型，人工神經網路定價模型，遺傳規劃定價模型等資料驅動模型之外的另一種具適應性學習能力的選擇權定價模式。 / The option pricing development rapid in recent years. However, the recent rapid development of theory and the application can be traced to the pathbreaking paper by Fischer Black and Myron Scholes(1973). In that pioneer paper, they provided the first explicit general equilibrium solution to the option pricing problem for simple calls and puts and formed a basis for the contingent claim asset pricing and many subsequent academic studies. Although the Black-Scholes option pricing model has enjoyed tremendous success both in practice and research, Nevertheless, it produce biased price estimates. So, many numerical algorithms have advanced to modify the basic model. I classified these traditional numerical algorithms and computational intelligence methods into two categories. Namely, the model-driven approach and the data-driven approach. The model-driven approach is built on several major assumptions. When these assumption hold, the option price usually can be described as a partial differential equation such as the Black-Scholes formula and can be solved numerically. Several numerical methods can be regarded as a member of this category. There are the Galerkin method, finite-difference method, Monte-Carlo method, etc. Another is the data-driven approach. The validity of this approach does not rests on the assumptions usually made for the model-driven one, and hence has a great flexibility in handling real world financial data. Artificial neural networks, genetic algorithms and genetic programming are a member of this approach. In my dissertation, I take a literature review about option pricing. I use artificial neural networks in S & P 500 index option and Taiwan stock call warrant pricing empirical study. On the other hand, genetic programming development rapid in recent three years, I modified the past model and contruct a data-driven genetic programming model. andThen, I usd it to S & P 500 index option empirical study. In the last, I combined genetic algorithms and weight-residual method to develop a option pricing model.

本論文主要是在agent-based計算經濟體系下，利用Holland(1975)所提的遺傳演算法(genetic algorithms)作為計算工具，分別探討連鎖店賽局及寡占市場廠商價格策略的生態演化。 在連鎖店賽局的研究中，藉由agent-based計算經濟分析掠奪性定價的特性，並進一步探討參賽者價格策略的共演化(co-evolutionary)特性，及多元均衡賽局中均衡移轉的動態過程。針對賽局中不同的不確定性進行模擬，結果顯示廠商長期總合行為是否穩定，和賽局中的不確定程度有相當的關聯。另外，弱獨占者和潛在競爭者的價格策略存在著共演化特性。在此演化賽局中，Nash均衡雖非穩定均衡解，但卻最常浮現在長期總合行為中。因此，Nsah均衡對agent-based演化賽局的結果而言，相當具有參考價值。在特定的不確定程度下，長期總合行為似乎只在某些特定的Nash均衡中徘徊。這些移轉途徑並不具有對稱性，甚至移轉速度也非對稱。本研究所呈現的演化結果跳脫一般對均衡的觀念，展現出傳統理論所無法預知的共演化特性，並呈現出非對稱的吸引環。 此外，同樣在Agent-based計算經濟下探討寡占市場廠商策略生態。本研究首先闡明N參賽者囚犯兩難重複賽局和N廠商寡占賽局之間的異同，經由寡占賽局廠商償付矩陣(payoff matrix)的狀態相依馬可夫移轉矩陣( state-dependent Markov transition matrix)性質，說明N廠商寡占賽局和N參賽者囚犯兩難重複賽局的差異。其次，透過三家廠商寡占賽局的模擬實驗，以遺傳演算法建構參賽廠商的適應性行為，分別以寡占市場生態上的表現型(phenotypes)和基因型(genotype)進行分析。20次模擬結果所呈現的最終市場狀態相當分歧，有形成吸引環的三廠商寡占市場、有收斂到價格戰的三廠商寡占市場。另外也成功的模擬出三廠商寡占市場演化至雙佔市場、甚或獨占市場的過程。但是，在眾多模擬中並沒有發現持續的勾結定價狀態，反而掠奪性價格是較主要的價格策略。這些結果相對於實際經濟社會中的寡占市場，給予一個活潑生動的範例。 / Recently, genetic algorithms have been extensively applied to modeling evolution game in agent-based computational economic.　While these applications advance our understanding of evolution game, they have generated some new phenomena that have not been well treated in conventional game theory. In the first topic, we shall systemize the study of one of these new phenomena, namely, coevolutionary instability. We exemplify the basic properties of coevolutionary instability by the chain store game, which is the game frequently used to study the role of reputation effects in economics.　In addition, we point out that, while, due to uncertainty effects, Nash equilibria can no longer be stable, and they can still help us predict the dynamic process of the game.　In particular, we can see that the dynamic process of the game is well captured by a few Nash equilibria and the transition among them.　A careful study can uncover several interesting patterns and we show the impact of uncertainty on these patterns. In the second topic, the relation between the N-person IPD game and the N-person oligopoly game is rigorously addressed.　Our analytical framework shows that due to the path-dependence of the payoff matrix of the oligopoly game, the two games in general are not close in spirit.　We then further explore the significance of the path-dependence property to the rich ecology of oligopoly from an evolutionary perspective.　More precisely, we simulated the evolution of a 3-person oligopoly game, and showed that the rich ecology of oligopoly can be exhibited by modeling the adaptive behavior of oligopolists with genetic algorithms.　The emergent behavior of oligopolists are presented and analyzed.　We indicate how the path-dependence nature may shed light on the phenotypes and genotypes coming into existence.

本研究的主要目的是希望喚起國內、外學者對演化科學在經濟學上的重視，結合電腦、生物科技、心理學與數學於經濟學中，希望對傳統經濟學上因簡化假設而無法克服的實際經濟問題，可以利用電腦模擬技術獲得解決，並獲取新知與技能。 本研究共有六章，第一章為緒論，敘述緣由與研究動機。第二章介紹傳統經濟學的缺失，再以資料掘取知識及智慧系統建構金融市場。第三章則介紹各種不同人工智慧的方法以模擬金融市場的投資策略。第四章建立無結構性變遷時間序列模型--交易策略電腦模擬分析，僅以遺傳演算法模擬金融市場的投資策略，分別由投資組合、交易成本、調適性、演化、與統計的觀點對策略作績效評分析。第五章則建立簡單的結構性變遷模型，分別由調適性與統計的觀點，採取遺傳演算法再對投資策略進行有效性評估分析。第六章則利用資料掘取知識與智慧系統結合計量經濟學的方法，建構遺傳演算法發展投資策略的步驟，以台灣股票市場的資料進行實証研究，分別就投資策略、交易成本、調適性與演化的觀點作分析。最後一章則為結論。 未來研究的方向有： 1. 其他各種不同人工智慧的方法的比較分析，如人工神經網路、遺傳規劃法等進行績效的交叉比較分析。 2. 利用分類系統(Classifier System)與模糊邏輯的方法，改善標準遺傳演算法對策略編碼的效率，並建構各種不同的複雜策略以符合真實世界的決策過程。 3. 建構其他人工時間資料的模擬比較分析，例如ARCH (Autoregressive Conditional Heteroskedasticity)模型、Threshold 模型、 確定性(Deterministic) 模型等其他時間序列模型與更複雜的結構性變遷模型。 4. 進一步研究遺傳演算法所使用的完整資訊(例如，各種不同指標的選取)。 5. 本研究係採用非即時分析系統(Offline System)，進一步研究即時分析系統 (Online Sysetem)在實務上是有必要的。 / Historically, the study of economics has been advanced by a combination of empirical observation and theoretic development. The analysis of mathematical equilibrium in theoretical economic models has been the predominant mode of progress in recent decades. Such models provide powerful insights into economic processes, but usually make restrictive assumptions and appear to be over simplifications of complex economic system. However, the advent of cheap computing power and new intelligent technologies makes it possible to delve further into some of the complexities inherent in the real economy. It is now feasible to create a rudimentary form of “artificial economic life”. First, we build the framework of artificial stock markets by using data mining and intelligent system. Second, in order to analyze competition among buyers and sellers in the artificial market, we introduce various methods of artificial intelligence to design trading rules, and investigate how machine-learning techniques might be applied to search the optimal investment strategy. Third, we create a miniature economic laboratory to build the artificial stock market by genetic algorithms to analyze investment strategies, by using real and artificial data, which consider both structural change and nonstructural change cases. Finally, we use statistical analysis to examine the performance of the portfolio strategies generated by genetic algorithms.