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.

本文採用可加性模型分析法建立台灣地區小型商用車市場之需求模型，並 引進Box-Jenkins時間序列模型處理具自我相關之誤差項，以利進行拔靴 推論設計時，能拔靴白干擾(bootstrapping white noise)，即重抽樣白 干擾的經驗分配。在此次研究過程中，除配適Box-Jenkins時間序列模型 外，所有分析步驟都是完全自動的，不須作假設和檢驗的工作，所以可降 低傳統上因統計人員主觀判斷錯誤所造成的估計偏誤。可加性模型改進傳 統迴歸模型須先假設模型形式的限制，可從商用車實證分析中，直接由資 料配適平滑函數，顯見其合理性。拔靴法免除傳統推論程序須強使隨機干 擾項分配為常態分配或漸近常態分配之束縛，改由殘差經驗分配模擬隨機 干擾項分配行為，在推論商用車市場上，也獲得不錯的結果。

Black and Scholes (1973)對於報酬率提出以B-S模型配適，但B-S模型無法有效解釋報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性的性質。Merton (1976)認為不尋常的訊息來臨會影響股價不連續跳躍，因此發展B-S模型加入不連續跳躍風險項的跳躍擴散模型，該模型可同時描述報酬率不對稱高狹峰和波動度微笑兩性質。Charles, Fuh and Lin (2011)加以考慮市場狀態提出狀態轉換跳躍模型，除了保留跳躍擴散模型可描述報酬率不對稱高狹峰和波動度微笑，更可以敘述報酬率的波動度叢聚和長記憶性。本文進一步拓展狀態轉換跳躍模型，考慮不連續跳躍風險項的帄均數與市場狀態相關，提出狀態轉換跳躍相關模型。並以道瓊工業指數與S&P 500指數1999年至2010年股價指數資料，採用EM和SEM分別估計參數與估計參數共變異數矩陣。使用概似比檢定結果顯示狀態轉換跳躍相關模型比狀態轉換跳躍獨立模型更適合描述股價指數報酬率。並驗證狀態轉換跳躍相關模型也可同時描述報酬率不對稱高狹峰、波動度微笑、波動度叢聚、長記憶性。最後利用Esscher轉換法計算股價指數選擇權定價公式，以敏感度分析模型參數對於定價結果的影響，並且市場驗證顯示狀態轉換跳躍相關模型會有最小的定價誤差。 / Black and Scholes (1973) proposed B-S model to fit asset return, but B-S model can’t effectively explain some asset return properties, such as leptokurtic, volatility smile, volatility clustering and long memory. Merton (1976) develop jump diffusion model (JDM) that consider abnormal information of market will affect the stock price, and this model can explain leptokurtic and volatility smile of asset return at the same time. Charles, Fuh and Lin (2011) extended the JDM and proposed regime-switching jump independent model (RSJIM) that consider jump rate is related to market states. RSJIM not only retains JDM properties but describes volatility clustering and long memory. In this paper, we extend RSJIM to regime-switching jump dependent model (RSJDM) which consider jump size and jump rate are both related to market states. We use EM and SEM algorithm to estimate parameters and covariance matrix, and use LR test to compare RSJIM and RSJDM. By using 1999 to 2010 Dow-Jones industrial average index and S&P 500 index as empirical evidence, RSJDM can explain index return properties said before. Finally, we calculate index option price formulation by Esscher transformation and do sensitivity analysis and market validation which give the smallest error of option prices by RSJDM.

退休金是退休人未來生活的依靠，確保在退休後能得到適足的退休給付，政府在退休金上實施保證收益制度，此制度為最低保證利率與投資報酬率連結。本文探討退休金給付標準為確定提撥制，當退休金的投資報酬率是根據其連結之股價指數的表現來計算時，股價指數報酬率的模型假設為馬可夫調控跳躍過程模型，考慮市場狀態與布朗運動項、跳躍項的跳躍頻率相關，即為Elliot et al. (2007) 的模型特例。使用1999年至2012年的道瓊工業指數與S&P 500指數的股價指數對數報酬率作為研究資料，採用EM演算法估計參數及SEM演算法估計參數共變異數矩陣。透過概似比檢定說明馬可夫調控跳躍過程模型比狀態轉換模型、跳躍風險下狀態轉換模型更適合描述股價指數報酬率變動情形，也驗證馬可夫調控跳躍過程模型具有描述報酬率不對稱、高狹峰及波動叢聚的特性。最後，假設最低保證利率為固定下，利用Esscher轉換法計算不同模型下型I保證之確定提撥制退休金的評價公式，從公式中可看出受雇人提領的退休金價值可分為政府補助與個人帳戶擁有之退休金兩部分。以執行敏感度分析探討估計參數對於馬可夫調控跳躍過程模型評價公式的影響，而型II保證之確定提撥制退休金的價值則以蒙地卡羅法模擬並探討其敏感度分析結果。 / Pension plan make people a guarantee life in their retirement. In order to ensure the appropriate amount of pension plan, government guarantees associated with pension plan which ties minimum rate of return guarantees and underlying asset rate of return. In this paper, we discussed the pension plan with defined contribution (DC). When the return of asset is based on the stock indices, the return model was set on the assumption that markov-modulated jump diffusion model (MMJDM) could the Brownian motion term and jump rate be both related to market states. This model is the specific case of Elliot et al. (2007) offering. The sample observations is Dow-Jones industrial average and S&P 500 index from 1999 to 2012 by logarithm return of the stock indices. We estimated the parameters by the Expectation-Maximization (EM) algorithm and calculated the covariance matrix of the estimates by supplemented EM (SEM) algorithm. Through the likelihood ratio test (LRT), the data fitted the MMJDM better than other models. The empirical evidence indicated that the MMJDM could describe the asset return for asymmetric, leptokurtic, volatility clustering particularly. Finally, we derived different model's valuation formula for DC pension plan with type-I guarantee by Esscher transformation under rate of return guarantees is constant. From the formula, the value of the pension plan could divide into two segment: government supplement and employees deposit made pension to their personal bank account. And then, we done sensitivity analysis through the MMJDM valuation formula. We used Monte Carlo simulations to evaluate the valuation of DC pension plan with type-II guarantee and discussed it from sensitivity analysis.

The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process. / The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.

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.

本文使用Esscher轉換法推導狀態轉換模型、跳躍獨立風險下狀狀態轉換模型及跳躍相關風險下狀態轉換模型的選擇權定價公式。藉由1999年至2011年道瓊工業指數真實市場資料使用EM演算法估計模型參數並使用概似比檢定得到跳躍相關風險下狀態轉換模型最適合描述報酬率資料。接著進行敏感度分析得知，高波動狀態的機率、報酬率的整體波動度及跳躍頻率三者與買權呈現正相關。最後由市場驗證可知，跳躍相關風險下狀態轉換模型在價平及價外的定價誤差皆是最小，在價平的定價誤差則略高於跳躍獨立風險下狀態轉換模型。 / In this paper, we derive regime switching model, regime switching model with independent jump and regime switching model with dependent jump by Esscher transformation. We use the data from 1999 to 2011 Dow-Jones industrial average index market price to estimate the parameter by EM algorithm. Then we use likelihood ratio test to obtain that regime switching model with dependent jump is the best model to depict return data. Moreover, we do sensitivity analysis and find the result that the probability of the higher volatility state , the overall volatility of rate of return , and the jump frequency are positively correlated with call option value. Finally, we enhance the empirical value of regime switching model with dependent jump by means of calculating the price error.