Fong與Vasicek（1997）提出風險分析應考慮敏感度分析、風險值及壓力測試，才能完整揭露投資組合的風險狀況。其中風險值的計算，不僅考慮二階風險，並且利用三階動差進行偏態修正。本文除了以變異數-共變異數法、歷史模擬法及蒙地卡羅模擬法此三種方法計算風險值，並利用Fong與Vasicek（1997）偏態修正法及Cornish-Fisher偏峰態修正法來做偏態及峰態的修正。而後再利用概似比檢驗法、回溯測試百分比法及Z檢定法作為驗證風險值模型的評比工具。我們建議在95%及99%的信賴水準下，求算風險值可利用Cornish-Fisher所提出的方法修正偏態及峰態。 / Fong and Vasicek (1997) mentioned that risk analysis should include sensitivity analysis, value at risk (VaR) and stress testing, in order to capture portfolio risk. The calculation of VaR should not only consider the second moment but should also adjust the skewness using the third moment. In this article, we determine VaR by employing three methods, the variance covariance, the historical simulation and the Monte Carlo simulation methods. In addition, we also adjust VaR for the skewness and kurtosis using the methods developed by Fong and Vasicek (1997) and Cornish-Fisher. Then, the likelihood ratio test, back testing and the Z-test are used to verify the VaR model. Our final test results suggest that calculating VaR should be adjusted for the skewness and the kurtosis as shown by the method proposed by Cornish Fisher in the 95% and 99% confidence intervals.

This research was driven by Theory of Reasoned Action (TRA) to examine the impact of ecological knowledge, ecological concern, and man-nature orientation on green purchasing (including both intention and actual behavior), with the moderating effect of price sensitivity and allowance and/or income. This research surveyed 602 Malaysian university students within the age bracket of 18 to 25, because this specific demographic is a sizeable market and such research is lacking in an emerging economy like Malaysia. The results demonstrated that ecological concern and man-nature orientation influenced purchase intention and actual purchase. The findings also indicated that price sensitivity and allowance and/or income moderated the relationship between behavioral intention and actual behavior. This study has two implications: (1) it extends TRA by exploring the potential moderating variables between behavioral intention and actual behavior, and its findings adds to the body of knowledge in the area of green consumer behavior; (2) marketing managers can formulate their green marketing strategies effectively by consistently driving heart-warming campaigns to create or stir consumers’ emotions. Marketers should keep in mind that Malaysians are highly influenced by man-nature relationship belief, and additionally, marketers need to be careful in justifying pricing difference between non-green and green products for consumers that are sensitive to price.

本研究的主要目的是檢視倒傳導神經網路是否具有人類在分類學習上所呈現出來的學習效應 — 競爭學習、遮蔽效應與不相關線索的影響。在實驗中，我們採用兩種倒傳導神經網路，來測試激發函數是否會影響倒傳導神經網路的學習。此兩種倒傳導神經網路分別採用sigmoid激發函數與hyperbolic-tangent激發函數。實驗結果顯示，以sigmoid為激發函數與以hyperbolic-tangent為激發函數的倒傳導神經網路都具有這三個學習效應。還有，以sigmoid為激發函數的倒傳導神經網路所呈現出來的學習效應比以hyperbolic-tangent為激發函數的倒傳導神經網路來得顯著。本研究的次要目的在於瞭解有效性（使用性）與敏感度分析的數值是否有對應關係。實驗結果顯示，線索A與線索B的敏感度分析數值差異可以反映出線索A與線索B的有效性差異。然而，敏感度分析數值卻無法準確地顯示線索的有效性數值。 / The main objective of this research is to examine whether back propagation neural networks (BP) have the learning effects found in human category learning — competitive learning, overshadowing and the deleterious of an irrelevant cue. Two kinds of BP, BP with sigmoid activation function and BP with hyperbolic-tangent activation function, are investigated to see if the activation function will make BP behave differently. According to the results of our experiments, these three learning effects are demonstrated both in BP with sigmoid and BP with hyperbolic-tangent, but they seems more significant in BP with sigmoid than in BP with hyperbolic-tangent. The second objective of our research is to see if there is a correspondence between the validity (the utilization) and the value of sensitivity analysis, R. From the results of our experiments, we observe that the difference between values of sensitivity analysis with respect to Cue A and Cue B reflects the difference of the validities between Cue A and Cue B. However, the value of sensitivity analysis does not show exactly what validity a cue is.

本篇論文旨在分析神經網路學習績效，並提出一套學習演算法，結合倒傳遞網路(BP)與理解神經網路(RN)，命名為RNBP，這套學習演算法將與傳統的BP做比較，以兩個不同的財務金融領域的應用，一個是選擇權上Black-Scholes訂價模式的模擬，一個是金融交換上利率的預測。主要績效的評估準則是以學習的效率與模擬、預測的準確度為依據。 此外，本論文的另一個重點是提出一套對於神經網路系統進一步分析的方法與工具，敏感度分析(Sensitivity Analysis)與滯留區(Dead Region)分析，藉以瞭解神經網路系統是否具有效地良好學習或被一般化的能力，從神經網路的角度來說，這也是BP與RNBP的另一個績效比較標準。本研究的結果顯示RNBP在預測準確度上較BP為優良，但是在學習效率與預測能力的穩定性上並沒有呈現一致性的結論；此外，敏感度分析與滯留區分析的結果也幫助神經網路在應用領域上有更深入的瞭解。 在過去，神經網路的應用者往往忽略了進一步瞭解神經網路的重要性與可行性，本論文的貢獻在於藉由分析神經網路所學習的知識，幫助應用者進一步瞭解神經網路表達的訊息在應用領域上所隱含的實質意義。 / The study attempts to analyze the learning performance of neural networks in applications, and propose a new learning procedure for the layered feedforward neural network systems, named KNBP, which binds RN and BP learning algorithms. Two artificial neural networks, BP and KNBP, here are both applied to two financial fields, the simulation of Black-Scholes pricing model for the call options and the midrates forecasting in financial swaps. The explicit performance comparison between the two artificial neural network systems is mainly based on two criteria, which are learning efficiency and forecasting effectiveness. Then we propound a mathematical methodology of sensitivity analysis and the dead regions to deeply explore inside the network structures to see whether the models of ANNS are actually well trained or valid, and thus setup an alternative comparable criterion. The results from this study show that RNBP performs better than BP in forecasting effectiveness, but RNBP obtains neither a consistent learning efficiency in cases nor a stable forecasting ability. Furthermore, the sensitivity analysis and the dead region analysis provide a deeper view of the ANNs in the applied fields. In the past, most studies applying neural networks ignored the importance that it is feasible and advantageous to obtain more useful information via analyzing neural networks. The purpose of the research is to help further understanding to the information discovery resulted from neural networks in practical applications.

本論文的研究目標是建構一個由多標記複合成的最佳疾病診斷工具，所考慮的評估準則為操作者特徵曲線在特定特異度範圍之線下面積(pAUC)。在常態分布假設下，我們推導多標記線性組合之pAUC以及最佳線性組合之必要條件。由於函數本身過於複雜使得計算困難。除此之外，我們也發現其最佳解可能不唯一，以及局部極值存在，這些情況使得現有演算法的運用受限，我們因此提出多重初始值演算法。當母體參數未知時，我們利用最大概似估計量以獲得樣本pAUC以及令其極大化之最佳線性組合，並證明樣本最佳線性組合將一致性地收斂到母體最佳線性組合。在進一步的研究中，我們針對單標記的邊際判別能力、多標記的複合判別能力以及個別標記的條件判別能力，分別提出相關統計檢定方法。這些統計檢定被運用至兩個標記選取的方法，分別是前進選擇法與後退淘汰法。我們運用這些方法以選取與疾病檢測有顯著相關的標記。本論文透過模擬研究來驗證所提出的演算法、統計檢定方法以及標記選取的方法。另外，也將這些方法運用在數組實際資料上。 / The aim of this work is to construct a composite diagnostic tool based on multiple biomarkers under the criterion of the partial area under a ROC curve (pAUC) for a predetermined specificity range. Recently several studies are interested in the optimal linear combination maximizing the whole area under a ROC curve (AUC). In this study, we focus on finding the optimal linear combination by a direct maximization of the pAUC under normal assumption. In order to find an analytic solution, the first derivative of the pAUC is derived. The form is so complicated, that a further validation on the Hessian matrix is difficult. In addition, we find that the pAUC maximizer may not be unique and sometimes, local maximizers exist. As a result, the existing algorithms, which depend on the initial-point, are inadequate to serve our needs. We propose a new algorithm by adopting several initial points at one time. In addition, when the population parameters are unknown and only a random sample data set is available, the maximizer of the sample version of the pAUC is shown to be a strong consistent estimator of its theoretical counterpart. We further focus on determining whether a biomarker set, or one specific biomarker has a significant contribution to the disease diagnosis. We propose three statistical tests for the identification of the discriminatory power. The proposed tests are applied to biomarker selection for reducing the variable number in advanced analysis. Numerical studies are performed to validate the proposed algorithm and the proposed statistical procedures.

許多公司在發行公司債的時候，會給此公司債一個可提前贖回的特性，此種公司債稱為可贖回公司債(Callable Bond)，用來規避利率變動風險的金融商品也與我們熟知的利率交換不同，稱為可取消利率交換(Cancelable Swap)。其實可取消利率交換可以拆解成百慕達利率交換選擇權(Bermudan Swaption)加上利率交換，由於利率交換之評價較簡單也有市場一致的評價方法，因此百慕達利率交換選擇權便成為評價的重點。 評價的部分，由於百慕達式的商品有提前履約的特性，造成其封閉解不存在，因此需要利用其他的近似解或是數值方法來求它的價格。由於本文採用BGM(1997)的市場利率模型(Libor Market Model)，其高維度的性質導致數狀方法與有限差分法使用起來較無效率，因此本文選擇使用蒙地卡羅法做為評價的方法，同時利用Longstaff and Schwartz(2001)的最小平方蒙地卡羅法(Least Squares Monte Carlo Method)來解決提前履約的問題。 最後，本文將採用2種利率波動度假設與2種不同利率間相關係數的假設，共4種組合，在歐式利率交換選擇權的市場波動度下進行校準，使用校準出來的參數進行評價來得到4種價格。再進行商品的敏感度分析(Sensitivity Analysis)和風險值(Value at Risk)的計算。

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.

Chen, Chang, Wen and Lin (2013)提出馬可夫調控跳躍過程模型(MMJDM)描述股價指數報酬率，布朗運動項、跳躍項之頻率與市場狀態有關。然而，利率並非常數，本論文以狀態轉換模型配適零息債劵之動態過程，提出狀態轉換下的利率與具跳躍風險的股票報酬之二維模型(MMJDMSI)，並以1999年至2013年的道瓊工業指數與S&P 500指數和同期間之一年期美國國庫劵價格為實證資料，採用EM演算法取得參數估計值。經由概似比檢定結果顯示無論道瓊工業指數還是S&P 500指數，狀態轉換下利率與跳躍風險之股票報酬二維模型更適合描述報酬率。接著，利用Esscher轉換法推導出各模型下的股價指數之歐式買權定價公式，再對MMJDMSI模型進行敏感度分析以評估模型參數發生變動時對於定價公式的影響。最後，以實證資料對各模型進行模型校準及計算隱含波動度，結果顯示MMJDMSI在價內及價外時定價誤差為最小或次小，且此模型亦能呈現出波動度微笑曲線之現象。 / To model asset return, Chen, Chang, Wen and Lin (2013) proposed Markov-Modulated Jump Diffusion Model (MMJDM) assuming that the Brownian motion term and jump frequency are all related to market states. In fact, the interest rate is not constant, Regime-Switching Model is taken to fit the process of the zero-coupon bond price, and a bivariate model for interest rate and stock index return with regime-switching and dependent jump risks (MMJDMSI) is proposed. The empirical data are Dow Jones Industrial Average and S&P 500 Index from 1999 to 2013, together with US 1-Year Treasury Bond over the same period. Model parameters are estimated by the Expectation-Maximization (EM) algorithm. The likelihood ratio test (LRT) is performed to compare nested models, and MMJDMSI is better than the others. Then, European call option pricing formula under each model is derived via Esscher transformation, and sensitivity analysis is conducted to evaluate changes resulted from different parameter values under the MMJDMSI pricing formula. Finally, model calibrations are performed and implied volatilities are computed under each model empirically. In cases of in-the-money and out-the-money, MMJDMSI has either the smallest or the second smallest pricing error. Also, the implied volatilities from MMJDMSI display a volatility smile curve.