給定兩個有限離散型條件分配，我們可以去探討有關相容性及唯一性的問題。Tian et al.(2009)提出一個統合的方法，將相容性的問題轉換成具限制條件的線性方程系統(以邊際機率為未知數)，並藉由 l_2-距離測量解之誤差，進而求出最佳解來。他們也提出了電腦數值計算法在檢驗相容性及唯一性時的準則。 由於 Tian et al.(2009)的方法是把邊際機率和為 1 的條件放置在線性方程系統中，從理論的觀點來看，我們認為該條件在此種做法下未必會滿足。因此，本文中將邊際機率和為 1 的條件從線性方程系統中抽離出來，放入限制條件中，再對修正後的問題求最佳解。 我們提出了兩個解決問題的方法：(一) LRG 法；(二) 干擾參數法。LRG 法是先不管機率值在 0 與 1 之間的限制，在邊際機率和為 1 的條件下，利用 Lagrange 乘數法導出解的公式，之後再利用 Rao-Ghangurde 法進行修正，使解滿足機率值在 0 與 1 之間的要求。干擾參數法是在 Lagrange 乘數法公式解中有關廣義逆矩陣的計算部份引進了微量干擾值，使近似的逆矩陣及解可快速求得。理論證明，引進干擾參數所增加的誤差不超過所選定的干擾值，易言之，由干擾參數法所求出的解幾近最佳解。故干擾參數法在處理相容性問題上，是非常實用、有效的方法。從進一步分析Lagrange 乘數法公式解的過程中，我們也發現了檢驗條件分配"理論"相容的充分條件。 最後，為了驗證 LRG 法與干擾參數法的可行性，我們利用 MATLAB 設計了程式來處理求解過程中的運算，並以 Tian et al.(2009)文中四個可涵蓋各種情況的範例來解釋說明處理的流程，同時將所獲得的結果和 Tian et al. 的結果做比較。 / Given two finite discrete conditional distributions, we could study the compatibility and uniqueness issues. Tian et al.(2009) proposed a unified method by converting the compatibility problem into a system of linear equations with constraints, in which marginal probability values are assumed unknown. It locates the optimum solution by means of the error of l_2 - discrepancy. They also provided criteria for determining the compatibility and uniqueness. Because the condition of sum of the marginal probability values being equal to one is in Tian et al.s’linear system, it might not be fulfilled by the optimum solution. By separating this condition from the linear system and adding into constraints, we would look for the optimum solution after modification. We propose two new methods: (1) LRG method and (2) Perturbation method. LRG method ignores the requirement of the probability values being between zero and one initially, it then uses the Lagrange multipliers method to derive the solution for a quadratic optimization problem subject to the sum of the marginal probability values being equal to 1. Afterward we use the Rao-Ghangurde method to modify the computed value to meet the requirement. The perturbation method introduces tiny perturbation parameter in finding the generalized inverse for the optimum solution obtained by the Lagrange multipliers method. It can be shown that the increased error is less than the perturbation value introduced. Thus it is a practical and effective method in dealing with compatibility issues. We also find some sufficient conditions for checking the compatibility of conditional distributions from further analysis on the solution given by Lagrange multipliers method. To show the feasibilities of LRG method and Perturbation method, we use MATLAB to device a program to conduct them. Several numerical examples raised by Tian et al.(2009) in their article are applied to illustrate our methods. Some comparisons with their method are also presented.

欲透過流動性調整模型來探討流動性風險對或有償權的影響，但本篇研究著重於選擇權的分析。根據Feng (2014)，流動性折現因子由市場流動性與股價對市場流動性敏感度所構成，而且此流動性之動態過程具有均數復歸的特性。根據本篇研究結果，價內選擇權和價平選擇權的評價表現比傳統Black-Scholes好，如果進一步將流動性之跳躍性質引入模型，除了價內選擇權和價平選擇權之外，價外選擇權的評價表現亦呈現大幅度的改善。於探討模型評價表現優劣之餘，本篇文章欲更進一步探究市場不流動性對選擇權避險參數的影響。 / This study uses a liquidity-adjusted pricing model to discuss the impact of the liquidity risk on Contingent Claim. However, we focus on the analysis of option. The liquidity discount factor consists of market liquidity and the sensitivity of stock prices to market illiquidity. The dynamic process of market liquidity possesses mean-reversion. Our empirical results show the liquidity model will improve pricing performance for ITM and ATM options. After incorporating diffusive jumps in liquidity, marked improvements in pricing performance for OTM options are observed. In addition, we discuss the impacts of liquidity risk on hedging parameters.

由於採用的地球原子不同，目前，台灣地區有兩種坐標系統存在，TWD67(Taiwan Datum 1967) 和TWD97(Taiwan Datum 1997)。在應用上，必須進行不同地球原子間之坐標轉換。坐標轉換方面，有許多方法可供選擇，如六參數轉換、支持向量機(Support Vector Machine, SVM)轉換等。 最小二乘支持向量機(Least Square Support Vector Machine, LSSVM)，為SVM的一種演算法，是一種非線性模型。LSSVM在運用上所需之參數少，能夠解決小樣本、非線性、高維度和局部極小點等問題。目前，LSSVM，已經被成功運用在影像分類和統計迴歸等領域上。 本研究將利用LSSVM採用不同之核函數：線性核函數(LIN)、多項式核函數(POLY)及徑向基核函數(RBF)進行TWD97和TWD67之坐標轉換。研究中並使用基因演算法來調整LSSVM的RBF核函數之系統參數(後略稱RBF+GA)，找出較佳之系統參數組合以進行坐標轉換。模擬與實測之地籍資料，將被用以測試LSSVM及六參數坐標轉換方法的轉換精度。 研究結果顯示，RBF+GA在各實驗區之轉換精度優於參數優化前RBF之轉換精度，且RBF+GA之轉換精度也較六參數轉換之轉換精度高。 進行參數優化後，RBF+GA相對於RBF的精度提升率如下：(1)模擬實驗區：參考點與檢核點數量比分別為1：1、2：1、3：1、1：2及1：3時，精度提升率分別為15.2%、21.9%、33.2%、12.0%、11.7%；(2)真實實驗區：花蓮縣、台中市及台北市實驗區之精度提升率分別為20.1%、32.4% 、22.5%。 / There are two coordinate systems with different geodetic datum in Taiwan region, i.e., TWD67 (Taiwan Datum 1967) and TWD97 (Taiwan Datum 1997). In order to maintain the consistency of cadastral coordinates, it is necessary to transform from one coordinate system to another. There are many coordinate transformation methods, such as, 2-dimension 6-parameter transformation, and support vector machine (SVM). Least Square Support Vector Machine (LSSVM), is one type of SVM algorithms, and it is also a non-linear model。LSSVM needs a few parameters to solve non-linear, high-dimension problems, and it has been successfully applied to the fields of image classification, and statistical regression. The goal of this paper is to apply LSSVM with different kernel functions (POLY、LIN、RBF) to cadastral coordinate transformation between TWD67 and TWD97. Genetic Algorithm will be used to find out an appropriate set of system parameters for LSSVM with RBF kernel to transform the cadastral coordinates. The simulated and real data sets will be used to test the performances, and coordinate transformation accuracies of LSSVM with different kernel functions and 6-parameter transformation. According to the test results, it is found that after optimizing the RBF parameters (RBF+GA), the transformation accuracies using RBF+GA are better than RBF, and even better than those of 6-parameter transformation. Comparing with the transformation accuracies using RBF, the transformation accuracy improving rate of RBF+GA are : (1) The simulated data sets: when the amount ratio of reference points and check points comes to 1:1, 2:1, 3:1, 1:2 and 1:3, the transformation accuracy improving rate are 15.2%, 21.9%, 33.2%, 12.0% and 11.7%, respectively; (2) The real data sets： the transformation accuracy improving rate of RBF+GA for the Hualien, Taichung and Taipei data sets are 20.1%, 32.4% and 22.5%, respectively.

臺灣在二十世紀中完成了人口轉型，特別是生育轉型的幅度與速度最為劇烈。也正因為生育轉型過於成功，臺灣此刻正面臨超低生育率導致的人口衰滅危機。近年來，人口學界針對生育率變遷，熱中於探討生育率的步調（tempo）與數量（quantum）效應，藉此瞭解時期生育率變遷的趨勢。 生育步調與數量的分析，本質上仍是時期性測量，未能真正瞭解年輪生育率的變遷，以致對於時期生育率趨勢的分析無法解決根本問題。這個現象，對於臺灣生育率研究特別必須加以處理。然而，臺灣雖然是人口資料的「寶庫」，有關生育的人口統計，卻只有存在於二十世紀下半葉，亦即，二十世紀前半葉的完整生育統計已經無法獲取。本研究試圖結合人口普查、戶籍統計，以及抽樣調查資料，運用參數式模型（parametric mode）和人口轉換（demographic translation）等人口分析方法，嘗試重建二十世紀完整的時期與年輪生育率，藉此，分析年輪生育率與時期生育率之間的變遷關係，最終瞭解未來生育率發展的可能後果。 / Demographic Transition has been completed during the middle of 20th century in Taiwan, and the extent and speed of transition are spectacularly rapid. Due to the over succeed of the demographic transition, lowest-low fertility pattern has stricken Taiwan society and probably led to a horrible extinction. Recently, in order to project the pattern of fertility rate, demographers endeavored to figure out how tempo and quantum effects contribute to fertility rate. Unfortunately, analysis of tempo and quantum effects is essentially periodic measurement. It leads no way to understand the pattern of cohort fertility in Taiwan. However, although Taiwan’s demographic statistics is well known as the world’s treasure trove, the fertility statistics are available for only 50 years. It means that we are not capable of having the first half 20th century’s fertility rate in Taiwan. We use demographic analytic methods such as parametric mode and demographic translation to analyze combined data which is constituted of census data, vital statistics, and survey data. The object of this research is to re-build the 20th century’s fertility rate in Taiwan. Once we have the intact fertility rate in 20th century, we could realize the pattern of period and cohort fertility transition. Furthermore, we will have a better chance to project Taiwan’s fertility rate in the future.

傳統參數隨機成本邊界模型需事先假設其函數型態，但真正的函數型態未知，若是假設錯誤的函數型態可能存在模型設定誤差，另外過去估計成本函數時，大多著重於技術效率的衡量，而忽略配置效率，如此一來，將導致模型參數估計產生偏誤，影響後來效率的計算。基於上述的問題，本研究將應用半參數隨機成本邊界模型且同時考量技術效率與配置效率，不但函數設定具有彈性且能正確的衡量效率值，然而在考量配置效率的衡量後，增加模型估計的困難度，使得估計收斂不易，因此本研究提出一個五階段的估計步驟，應用蒙地卡羅模擬進行分析，該估計步驟不但能簡化估計且能得到技術與配置效率的一致性估計。最後則將本研究提出的估計方法應用在實證研究上，探討14個東歐國家在轉型期間其技術與配置效率的衡量，使用不平衡縱橫資料，共340家商業銀行進行實證分析。 / Conventional parametric stochastic cost frontier models are likely to suffer from biased inferences due to misspecification and the ignorance of allocative efficiency (AE). To fill up the gap in the literature, this article proposes a semiparametric stochastic cost frontier with shadow input prices that combines a parametric portion with a nonparametric portion and that allows for the presence of both technical efficiency (TE) and AE. The introduction of AE and the nonparametric function into the cost function complicates substantially the estimation procedure. We develop a new estimation procedure that leads to consistent estimators and valid TE and AE measures, which are proved by conducting Monte Carlo simulations. An empirical study using unbalanced panel data on 340 commercial banks from 14 East European countries over the period 1993-2004 is performed to help shed some light on the usefulness of our procedure.

近年來有許多研究發現，適應性管制圖在偵測製程或產品幅度偏移時的速度比傳統的舒華特管制圖來的快，許多文獻也討論到利用適應性管制技術同時監控製程的平均數和變異數。隨著科技的發達，許多產品在製造上更加精密，現今普遍使用的固定參數管制圖並無法有效率的偵測出製程失控，導致巨大的成本損失。為了改善現有管制圖的偵測效率與有效控制製程失控下的損失，我們提出了三種適應性加權損失管制圖，包括變動抽樣間隔(VSI)、變動樣本數與抽樣間隔(VSI)、變動管制參數(VP)來偵測單一製程與兩相依製程的平均數和變異數。採用製程發生變動後到管制圖偵測出異常訊息所需的平均時間(AATS)與所需的總觀測數(ANOS)來衡量管制圖的偵測績效，並利用馬可夫鏈推導計算得之。從數值分析中發現，適應性加權損失管制圖在「偵測小偏移幅度時的偵測效率」與「成本的控制」明顯比傳統管制圖表現的更好，再加上每一個製程僅需採用單一管制圖，對使用者也較為簡便並且容易理解，因此適應性加權損失管制圖在實務上是值得被推薦使用的。 / Recent research has shown that control charts with adaptive features detect process shifts faster than traditional Shewhart charts. In this article, we propose three kinds of adaptive weighted loss (WL) control charts, variable sampling intervals (VSI) WL control charts , variable sample sizes and sampling intervals (VSSI) WL control charts and variable parameters (VP) WL control charts, to monitor the target and variance on a single process step and two dependent process steps simultaneously. These adaptive WL control charts may effectively distinguish which process step is out-of-control. We use the Markov chain approach to calculate the adjusted average time to signal (AATS) and average number of observations to signal (ANOS) in order to measure the performance of the proposed control charts. From the numerical examples and data analyses, we find the adaptive WL control charts have better detection abilities and performance than fixed parameters (FP) WL control charts and FP Z(X-bar)-Z(Sx^2) and Z(e-bar)-Z(Se^2) control charts. We also proposed the optimal adaptive WL control charts using an optimization technique to minimize AATS when users cannot specify the values of the variable parameters. In addition, we discuss the impact of misusing weighted loss of outgoing quality control chart. In conclusion, using a single chart to monitor a process is inherently easier than using two charts. The WL control charts are easy to understand for the users, and have better performance and detection abilities than the other charts, thus, we recommend the use of WL control charts in the real industrial process.

隨著資訊科技的發展，筆記型電腦已經愈來愈普及，且價格不再高不可攀，消費者在選購電腦時，會以筆記型電腦取代桌上型電腦，因此消費者的購買意願增加，如何吸引消費者的購買意願，是目前許多企業所面臨的問題。消費者在購買產品前所考慮因素以品質最為重要。電腦公司若能提供品質保證，勢必能增加消費者購買的意願。 筆記型電腦為高精密與高價值的產品，攜帶方便為此產品的特色。由於攜帶方便的特性，顧客可以攜帶著筆記型電腦工作，因此一時的疏忽常對筆記型電腦造成損害，其中以外力所造成之損害最為嚴重，包括衝擊碰撞與摔落碰撞。 本研究以北縣某筆記型電腦製造公司之客戶維修資料與公司摔落測試之統計，以液晶螢幕燈管和玻璃損壞之成本最高。所以本論文主要目的希望能研究出筆記型電腦摔落之最佳保護設計，減低摔落所造成之損壞。針對研究之筆記型電腦抗摔落問題規劃防摔角墊實驗以收集相關數據，並利用以下六種不同的分析方法，(1)變異數分析結合迴歸分析方法、(2)田口方法、(3)田口損失函數法、(4)倒傳遞類神經網路法、(5)模糊結合TOPSIS法與(6)模糊結合類神經網路法，分別決定最適防摔角墊組合，並比較其最適防摔角墊組合之異同。倘若這六種分析方法結果不盡相同，則再規劃實驗以求得最適角墊硬度與面積，得到最適防摔角墊組合。

本文的研究目的在於探討百慕達利率交換選擇權以及CMS結構型債券的評價與分析。在利率風險管理的工具中，利率交換(IRS)可說是最重要的一項，由於利率交換契約提供了很有效率的資產負債管理方式，自1980年代出現利率交換以來，利率交換的交易量與日遽增。在國內利率市場發展上，本國證券商在86年核准證券自營商、承銷商得因業務需要，可以進行避險性的新台幣利率交換交易。主管機關已在90年10月開放證券商經營利率交換業務。91年6月財政部又開放證券商可進一步承作更多樣化的利率商品，包括利率選擇權、利率交換選擇權、遠期利率協定及上述商品之組合。故本文提出之百慕達式利率交換選擇權個案分析，期能探討利率交換選擇權的評價方式及其避險方式。 對於市場上的個體投資戶而言，要如何利用自身對利率走勢的判斷來獲取利潤? 除了衍生性利率商品的操作外，目前還可以投資利率連結型債券，本文以CBA發行之六年期固定期限交換利率連動債券為例，進行個案的評價與避險分析，期能提供券商在未來設計與發行此類型利率連動債券時的一個參考。

Brigo與Mercurio提出了三種新的資產價格過程，分別是位移CEV過程、位移對數常態過程與混合對數常態過程。在這三種過程中，資產價格的波動度不再是一個固定的常數，而是時間與資產價格的明確函數。而由這三種過程所推導出來的歐式選擇權評價公式，將會導致隱含波動度曲線呈現傾斜曲線或是微笑曲線，且提供了參數讓我們能夠配適市場的波動度結構。本文利用台指買權來實證Brigo與Mercurio所提出的三種歐式選擇權評價公式，我們發現校準結果以混合對數常態過程優於位移CEV過程，而位移CEV過程則稍優於位移對數常態過程。因此，在實務校準時，我們建議以混合對數常態過程為台指買權的評價模型，以達到較佳的校準結果。 / Brigo and Mercurio proposed three types of asset-price dynamics which are shifted-CEV process, shifted-lognormal process and mixture-of-lognormals process respectively. In these three processes, the volatility of the asset price is no more a constant but a deterministic function of time and asset price. The European option pricing formulas derived from these three processes lead respectively to skew and smile in the term structure of implied volatilities. Also, the pricing formula provides several parameters for fitting the market volatility term structure. The thesis applies Taiwan’s call option to verifying these three pricing formulas proposed by Brigo and Mercurio. We find that the calibration result of mixture-of-lognormals process is better than the result of shifted-CEV process and the calibration result of shifted-CEV process is a little better than the result of shifted-lognormal process. Therefore, we recommend applying the pricing formula derived from mixture-of-lognormals process to getting a better calibration.

摘要 本研究主要利用誤差偵測方法發掘數值高程模型中可能出現的高程誤差，藉以提升數值高程模型之高程品質。本研究採用三種誤差偵測方法即參數統計、水流方向矩陣、坡度與變化約制等，這三種方法過去是應用在航測資料測製之格網式數值高程模型，本研究嘗試推廣至空載光達製作的數值高程模型。 利用模擬DEM資料以驗證三種偵測方法之偵測能力。首先利用多項式函數擬合出各種地形，並假設該地形無誤差。再將人為誤差隨機加入模擬DEM資料；第二部份則將誤差偵測之方法應用至真實的數值高程模型資料，並配合檢核點高程測量檢驗之。根據誤差偵測結果，參數統計和坡度變化結果類似而且皆有過度偵測之缺點，可透過提高門檻值或高通濾波改善；水流方向矩陣比較不適合誤差偵測，但可透過窪地填平最佳化地形。 關鍵字：數值高程模型、誤差偵測、參數統計法、坡度與變化約制、水流方向矩陣。 / Abstract In this study, error detection methods were proposed to find possible elevation errors in digital elevation model (DEM), and to improve the quality of DEM. Three methods were employed to detect errors in the study, i.e. parametric statistical method, flow direction matrix, and constrained slope and change. These methods can deal with grid DEM from photogrammetric approach in the past, and now the methods are used to find errors in high resolution DEM from light detection and ranging (LIDAR). The simulated DEMs were used to approve the detection capability of the proposed methods. The fitted DEMs were first obtained by polynomial functions fit the different terrains and assuming these DEMs were free of errors. Then the artificial errors were added to fitted DEMs. The proposed methods were also applied to real DEM data got from LIDAR and field check works were run to insure the results. The results of parametric statistical method and constrained slope and change are similar, and all show the over-detection of errors. These results can be improved by using high threshold or high-pass filter. Flow direction matrix is not suitable for error detection in DEM, but can be applied to fill sink to optimize terrain for watershed analysis. Keyword: digital elevation model, error detection, parametric statistical method, constrained slope and change, flow direction matrix.