過去的三十年間由於評價美式選擇權所產生的自由邊界問題已經有相當的研究成果。本論文將證明自由邊界問題的解為遞增函數。更進一步提出自由邊界凹性的嚴謹証明。利用我們的結論可以得知美式選擇權的最佳履約邊界對時間而言為嚴格遞減的凹函數。這個結果對可用來求導最佳履約邊界的漸近解。 對於美式交換選擇權，我們將其自由邊界問題轉換成單變數的積分方程，同時提供一個永續型美式交換選擇權的評價公式。對於有限時間的美式交換選擇權的最佳履約邊界，我們將提供一個接近到期日的漸近解並發展一個數值方法求其數值解。數值計算的結果顯示漸近解在接近到期日時與數值解非常接近。 對於評價美式選擇權，我們提出使用混合整數非線性規劃(MINLP)的模型，這個模型的最佳解同時提供賣方的完全避險策略、買方的最佳交易策略與美式選擇權的公平價格。因為求算MINLP模型的解需耗用大量的計算時間，我們證明此模型和其非線性規劃的寬鬆問題有相同的最佳解，所以只需求算寬鬆問題即可。觀察數值結果亦顯示非線性規劃的寬鬆問題可以大幅的降低計算的時間。此外，當市場的價格低於公平價格時，我們提出一個最小化賣方期望損失的數學規劃模型，此模型的解提供賣方最小化其期望損失的避險策略。 / In the past three decades, a great deal of effort has been made on solving the free boundary problem (FBP) arising from American option valuation problems. In this dissertation, we show that the solutions, the price and the free boundary, of this FBP are increasing functions. Furthermore, we provide a rigorous verification that the free boundary of this problem is concave. Our results imply that the optimal exercise boundary of an American call is a strictly decreasing concave function of time. These results will provide a useful information to obtain an asymptotic formula for the optimal exercise boundary. For pricing of American exchange options (AEO), we convert the associated FBP into a single variable integral equation (IE) and provide a formula for valuating the perpetual AEO. For the finite horizon AEO, we propose an asymptotic solution as time is near to expiration and develop a numerical method for its optimal exercise boundary. Compared with the computational results, the values of our asymptotic solution are close to the computational results as time is near to expiration. For valuating American options, we develop a mixed integer nonlinear programming (MINLP) model. The solution of the MINLP model provides a hedging portfolio for writers, the optimal trading strategy for buyers, and the fair price for American options at the same time. We show that it can be solved by its nonlinear programming (NLP) relaxation. The numerical results reveal that the use of NLP relaxation reduces the computation time rapidly. Moreover, when the market price is less than the fair price, we propose a minimum expected loss model. The solution of this model provides a hedging strategy that minimizes the expected loss for the writer.

To date there is little evidence on the effect of property-liability (P-L) insurer's business strategy and organizational structure change on their frontier efficiency performance and productivity change. This issue is important since traditional theory assumes firms that minimizes cost and maximizes profit with more efficient strategy will survive in the long run. The main goal of this dissertation is to examine the efficiency performance in the U.S. P-L insurance industry using frontier efficiency and productivity methods. This dissertation consists of three essays on the efficiency studies. The first essay uses the data envelopment analysis to examine the efficiency performance and economies of scope for nonspecialists and specialists in the U.S. P-L insurance industry. The empirical evidence suggests that nonspecialists (specialists) dominate specialists (nonspecialists) in producing nonspecialists (specialists) input–output vectors and provide evidence for the coexistence of economies of scope and diseconomies of scope in the U.S. P-L insurance industry. Our second essay uses the stochastic frontier analysis to examine whether nonspecialized strategy dominates specialized strategy in the U.S. P-L insurance industry. The empirical evidence supports that both the nonspecialized hypothesis and the specialized hypothesis hold for different types of P-L insurers. Our third essay investigates whether the conversion of U.S. P-L insurers improves their efficiency performance before and after conversion. The empirical evidences of the value-added approach and the financial intermediary approach indicate that converting insurers experience improvement in their efficiency relative to mutual counter samples after the conversion, supporting the efficiency hypothesis proposed by Mayers and Smith (1986). Overall, the evidence of this dissertation shows that P-L insurer's diversification strategy and organizational structure change has significant impact on their frontier efficiency performance and productivity change.

在這篇論文中，我們討論的是一階非線性衝擊動態方程的週期邊界值問題。利用Schaefer定理及Banach固定點定理，我們得到一些解的存在性結果。 / In this thesis, we are concernd with nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales. By using Schaefer’s theorem and Banach’s fixed point theorem we acquire some new existence results.

地方稅捐稽徵機關績效之良窳攸關地方政府庫收，更直接影響地方經濟成長、資源配置效率與所得分配之公平；本文試圖採用能排除外在因素與隨機干擾之三階段產出導向資料包絡分析法（以下簡稱DEA），針對23個地方稅捐稽徵機關2004年迄2008年資料進行管理效率評估，再以隨機邊界分析法（以下簡稱SFA）分離外生因素及隨機干擾以調整各機關產出至相同基準後，再評估排除外在與隨機干擾因素的管理效率。 未考慮外生因素與隨機干擾的DEA效率評估結果顯示，有高達88.7%及82.6%的地方稅捐稽徵機關分別於技術效率及純技術效率上尚有改善空間。第二階段SFA估計結果顯示，土地移轉現值、機關內大專畢業以上員額之比例及員額平均年齡對管理效率皆有正向影響；而總統大選期間及有高鐵停靠站之縣市除對部分產出無顯著影響外，對管理效率之提升亦具優勢；然而，服務轄區土地面積與實徵淨額之效率呈負相關，卻與違章漏稅裁罰效率呈正相關；地方首長選舉期間除為避免清理欠稅招致民怨而降低技術效率外，對其他管理效率則皆呈正相關；又都市計畫面積占稽徵區域比例與地方稅實徵淨額之管理效率呈正相關，卻與欠稅清理效率呈負相關。調整後之DEA結果顯示各項效率值與調整前比較皆存在顯著差異，顯示排除外生因素與隨機干擾影響以避免效率值被錯估確有其必要性；但仍有高達93.05%及68.7%之地方稅捐稽徵機關分別於技術效率及純技術效率上存有改善空間；又多數稽徵機關處於規模報酬遞增階段，即產能過剩而造成資源浪費。另與財政部稽徵業務考核成績比較分析，在規模效率平均值排名方面，除臺南市外，甲組機關排名普遍優於乙組機關；但純技術平均效率值之排名卻有一半以上之甲組機關表現反而不如部分乙組受評單位；顯示甲、乙組之分類歷經多年仍沿襲舊有分組將使各機關未能於適合之群組中受考而錯估其績效。 基於上述實證研究結果，本文提出下列政策性建議： 一、建議逐期分階段調整人力及預算至最適規模，以善加運用資源降低產能過剩情形。 二、建議各機關應引用環保之共乘概念，加強政府機關間橫向溝通、聯繫與合作。 三、若情況允許，建議可不區分甲乙組針對全體地方稅捐稽徵機關進行考核。若人力、時間或其他情況不允許，建議研擬具體方案隨各機關規模改變而有重新分級之機制。 四、建議甲組機關亦可選擇純技術效率較佳之乙組機關作為觀摩學習之對象。 五、建議財政當局可考慮將外在因素之影響納入評核，以提升考核之信度與效度。 最後，臺灣自2010年底起將有部分縣市改制為直轄市，考核編組方式勢將有所變革，有待後續研究者追蹤探討；而改制後所引起之資源重分配亦可作為未來之研究議題。 / The Performance of Local Tax Bureaus is relevant to the revenue of Public Treasury, and even has direct impacts on local economic growth, efficiency of resource allocation and equity of income distribution. This paper attempts to use three-stage out-oriented DEA which can rule out the external factors and the statistical noises to evaluate the efficiency of 23 Local Tax Bureaus in Taiwan during the period of 2004 to 2008. After measuring slack variables of each Bureau in the first stage, the Stochastic Frontier Analysis (SFA) model is used to separate the external factors from the statistical noises, and then adjust the output of each Bureau to the same benchmark. Finally, DEA is again used to evaluate the efficiency of 23 Local Tax Bureaus. The DEA efficiency evaluation results in the first stage show that up to 88.7% and 82.6% of the Local Tax Bureaus still have an ample room to improve their technical and pure technical efficiency. In the second stage, the SFA model estimates show that “the present value of land transfer”, “the proportion of post-graduates in the Bureaus” and “the average age of the staff” have positive effects on the efficiency. “The period of Presidential Election” and “the cities or counties that Taiwan High Speed Rail have set station up” have insignificant impact on part of the outputs, but still have the advantages to enhance the efficiency. However, “the expanse of land in service area” has a negative correlation with the efficiency of net taxation, but is positively related to the efficiency with the fine of illegal tax evasion. “The election period of Local County Executive” has a positive correlation with the efficiency except that tax arrears liquidation might reduce technical efficiency. “The ratio of urban-planed area to the tax levy regional” and the efficiency of net taxation are positively correlated, but negatively related to the efficiency of tax arrears liquidation. After excluding external factors and the statistical noises, the third-stage DEA evaluation results are significantly different from those in the first stage, indicating that it is necessary to exclude impacts of external factors and statistical noises in order to avoid the misjudged value of efficiency. There are still as high as 93.05 % and 68.7% of the Local Tax Bureaus have an ample space for improvement respectively on technical efficiency and pure technical efficiency. Most of the Tax Bureaus are at the increasing return of scale stage, implying that the surplus of capacity cause the waste of resources. Finally, compared with the performance evaluation held by Ministry of Finance, the empirical results in this study show that although the classification of Local Tax Bureaus has been adopt for many years, Bureaus’ performance evaluation results might be misjudged in the unsuitable group. Based on the above empirical results, this research attempts to propose the following policy suggestions: 1. It is recommended to adjust the phase of manpower and budget to the optimum scale for the best using of resources and to reduce inefficiency of excess capacity. 2. Enhancing horizontal communication among government agencies may improve the efficiency of Local Tax Bureaus. 3. If possible, it is recommended to evaluate Local Tax Bureaus without classification. If not, a mechanism of re-rating according to the scale change of Local Tax Bureaus may be needed. 4. It is proposed that Local Tax Bureaus of Group A can take lesson from those of Group B with better pure technical efficiency to learn from. 5. It is suggested that government authorities have to exclude the effect of external factors to improve the reliability and validity of performance evaluation. At the end of year 2010, several counties will be restructured in municipalities. The classification of Local Tax Bureaus for performance assessment must be changed. The reallocation of resources caused by restructuring may be used in future studies.

本文採民國94、96、98、100、102年的台灣 「人力運用調查」 資料庫, 以關聯結構法找出組合誤差間的關聯結構密度函數與聯合機率密度函數, 建構隨機邊界關聯結構模型, 解決勞動市場上樣本選擇性問題。 之後分別針對男性及女性估計薪資方程式, 探討每位勞工的薪資效率程度。 本文男、 女性的勞工各按年齡、 工作經驗、 職業、 行業、 教育程度、 公司規模、 工作身分、 婚姻狀態、 工作地分為9大類, 在各類中分群比較薪資效率。 實證結果顯示, 公司規模、 工作身分、 工作地等 3 類, 不論有無考慮樣本選擇, 同一性別中的薪資效率變動趨勢大致一致, 但其餘 6 類, 有考慮樣本選擇的薪資效率變動明顯不同於未考慮樣本選擇。 在考慮了樣本選擇之後的實證結果大多打破以往文獻的預期, 可能是因為過往文獻探討薪資效率時, 大多未考慮樣本選擇, 即將無工作者樣本完全排除, 導致迴歸分析結果僅適用於有工作者。 除了探討薪資效率外, 本文也嘗試在隨機邊界法的架構下, 提出一個衡量性別歧視的新觀點, 將兩性薪資無效率的差異視為一種性別歧視。 若以新觀點衡量台灣的勞動市場, 會發現這5個年度中, 薪資差異幾乎可以完全歸諸於性別歧視。 這顯示即使兩性的薪資差異雖然逐年縮小, 但性別的刻板印象仍存於當今的台灣勞動市場, 造成明顯的性別歧視。 / This paper adopts the "Manpower Utilization Survey" data, a database conducted by Directorate General of Budget, Accounting & Statistics, Executive Yuan, ROC (DGBAS), to study the issues of gender wage differentials and underpayment. The econometric model considers sample selection under the framework of the stochastic frontier model with copula methods. It requires to correct for sample selection and derive the copula density function and joint probability density function by copula method. We separately estimate the male and female wage equations, respectively, to evaluate the wage efficiency and decompose the average wage differential between male and female into several components. The paper distinguishes workers into 9 categories, including age, experience, occupation, industry, education, firm size, working identity, marital status and working area, and compares the wage efficiency between those categories. The empirical results shows that, the trend of wage efficiency in the categories of firm size, working identity, and working area are almost the same in each gender whether correcting for the sample selection bias or not. However, in the remaining 6 categories, the wage efficiency changes substantially after correcting the sample selection bias. With the correction of the sample election bias, most of the findings differ from those from the past literatures. This may be attributed to the fact that the past works mainly focus on employed workers and lead to possible sample selection bias. The paper also tries to offer a new method to measure the gender discrimination, which considers the difference in wage inefficiency between the male-female inefficiency as an element of discrimination. The paper finds that the wage differential between male and female can explain almost the entire discrimination. This findings confirms that the gender discrimination still exists in the Taiwan’s labor market eventhough the wage differential between male and female decreases over time.

當創新總是發生在不同專業領域的交界之處，團隊成員之間有效的知識互動便成為組織維持其競爭優勢的必要因素，因此為了持續創新，團隊成員必須克服不同專業領域所存在的知識邊界障礙，以便能夠整合團隊成員的知識與專長。在資訊系統的開發過程中，系統分析階段是觀察系統分析人員與使用者知識互動的最佳情境，因此本研究首先探索系統分析情境下影響互動雙方知識分享意願的前因，即創新氣氛與互動雙方的互動投入程度，並檢測這些因素之間的關係及影響。其次，本研究彙整四類邊界物件的內容，即語法的、語意的、實務的與隱喻的邊界物件，探討不同類別的邊界物件之間的關係及對專案創意的影響，並更進一步探究互動雙方的知識分享意願對各類邊界物件的影響。 研究樣本來自258位學生所扮演的系統分析人員及258位業界使用者，研究結果發現創新氣氛會同時影響系統分析人員與使用者的知識分享意願。當系統分析人員的互動投入程度越高，使用者的互動投入程度也會提高。使用者的互動投入程度會正向影響系統分析人員及使用者自身的知識分享意願；但是系統分析人員的互動投入程度卻對使用者的知識分享意願產生直接且負向的影響。 此外，系統分析人員的知識分享意願只對隱喻的邊界物件有正向影響，而使用者的知識分享意願卻對這四類邊界物件皆無顯著影響。在這四類邊界物件之中，只有實務的邊界物件對專案創意具有正向的影響，而隱喻的邊界物件則對於語法的、語意的、實務的邊界物件三者具有正向的影響，因此隱喻的邊界物件可以藉由實務的邊界物件對專案創意產生正向的間接效果。出乎意料之外，語意的邊界物件對專案創意具有負向的影響。在實務方面，本研究建議組織應該藉由增加實務的邊界物件和隱喻的邊界物件，以提高專案創意嶄露的可能性。 / As innovation happens from the boundaries between different specialty domains, effective knowledge interaction among participants has become a competitive necessity for organizations. In order to improve innovation, it is necessary for participants to deal explicitly with the interpretive barriers and further synthesize their expertise. During the development of information system, most knowledge interactions, which are conducted by systems analysts and users, can be observed in the phase of systems analysis. Thus, this study intends to explore not only factors that may affect participants’ intention to share knowledge, but also types of boundary objects in the context of systems analysis. As an innovative organizational climate and participants’ interaction involvement are identified as antecedents of participants’ intention to share knowledge, the relationships among these factors are studied. Besides, while four types of boundary objects are summarized, their effects on project innovativeness are discussed. Then, the influence of participants’ intention to share knowledge on the occurrence of four types of boundary objects was further examined. The results, based on data collected from 258 student analysts and 258 users, indicate that an innovative climate positively and directly influences both systems analysts and users’ intention to share knowledge. While systems analysts’ interaction involvement has a strong influence on users’ interaction involvement, which is measured by responsiveness, perceptiveness and attentiveness, users’ interaction involvement also has positive effects on both systems analysts and users’ intention to share knowledge; unexpectedly, systems analysts’ interaction involvement is negatively related to users’ intention to share knowledge. In addition, while systems analysts’ intention to share knowledge only influences the occurrence of metaphoric boundary objects, users’ intention to share knowledge does not demonstrate any significant effect on four types of boundary objects. Out of syntactic, semantic, pragmatic and metaphoric boundary objects, only pragmatic boundary objects had a strong positive effect on project innovativeness. As metaphoric boundary objects are shown to have positive effects on all other three types of boundary objects, metaphoric boundary object affects project innovativeness indirectly through pragmatic boundary objects. Surprisingly, semantic boundary objects negatively affects project innovativeness, although not very strongly. A practical implication is the possibility of increasing project innovativeness by enhancing both pragmatic boundary objects and metaphoric boundary objects.

本研究發展新的計量方法，運用隨機邊界法將單調性和曲度條件等性質納入迴歸模型，使用聯立迴歸模型進行估計，藉此讓係數估計值不易出現違反經濟理論的情況。 採用台灣2002年至2015年，51家商業銀行進行實證分析，發現本研究方法估計產出方向距離函數時，僅有5%以下的樣本點不符合單調和曲度等性質，用於估計產出面距離函數時，僅有2%以下的樣本點不符合。進一步探討台灣銀行業之非意欲產出--逾期放款--對估計技術效率的影響，顯示不考慮此非意欲產出造成整體銀行業、非金控本國銀行與外商銀行的技術效率被高估，而金控本國銀行的技術效率則被低估，此外，分析2007年金融風暴前後銀行業經營效率變化，顯示考慮非意欲產出銀行業經營效率顯著提升，然而，未考慮非意欲產出銀行業經營效率卻下降，兩者結果有著極大的差異。 / The aim of the paper is to develop a new approach, which is stochastic frontier analysis imposing monotonicity and curvature conditions, then using simultaneous regression model to estimate. By the approach, it can solve the problem of most of the coefficient estimates violating the economic theory. The study uses the data of 51 commercial banks in Taiwan from 2002 to 2015 to conduct the empirical analysis. It indicates that by output directional distance function, less than 5% sample points violate the monotonicity and curvature conditions; by output distance function, less than 2% sample points don’t obey the restricted conditions. Further, the paper discusses the effect of commercial banks’ undesirable output- non-performing loan- on estimating technical efficiency. The results show that ignoring the undesirable output cause the technical efficiency of overall banks, non-finance holding banks and foreign banks are overvalued, and the technical efficiency of finance holding banks are undervalued. Furthermore, analyze the change of business efficiency after financial crisis in 2007. It points out that using the model consider the undesirable output, the banks’ efficiency rises. However, using the model no consider the undesirable output, the banks’ efficiency decreases. There is an extremely conflict between two approach.

綜觀國內外探討金融產業經營效率之相關文獻，多數針對銀行、證券、保險中其一產業進行獨立實證研究，較無法將金融控股之綜效表現加以捕捉並體現在估計效率值中，也因此在本文中，將同時涵蓋銀行業務與證券業務，並以納入金控體制與否加以區分為不同子集合進行探討，透過數理方法聯結金控體制下銀行與證券業務部門兩者間因多角化經營所產生之綜效，以修正傳統方法上表現綜效法上之不足，使估計效率值具有更高的參考依據。 此外，研究產業效率所參考之研究方法，在相關文獻中無參數法乃以資料包絡分析法(Data envelopement analysis, DEA)為多數研究者所採用；參數法則以隨機邊界模型(stochastic frontier approach, SFA)為主要研究方法，進一步在不同群組技術效率之比較中，Battese et al. (2004) 與 O’Donnell et al. (2008)提出為多數研究者所接受之共同邊界模型(Metafrontier)，而Huang et al. (2013)所提出之修正模型使共同邊界模型在效率研究上更加完備，本文則希望以此修正模型作為主要研究模型，並同時引用Battese et al. (2004)傳統模型加以比較：(1)考慮綜效前後 (2)傳統模型與修正模型間效率值的差異，期待為後續相關研究者在方法論上提供參考依據。 關鍵字：經營效率、技術效率、共同邊界、計量方法、關聯結構法、金融控股銀行 / This study aims to discuss the evidence suggested that synergy improve the operating performance of Taiwan’s commerical banks and securites firms. Furthermore, efficiency comparisons amongst two basis metafrontier models, Haung et al.(2013) and Battese et al.(2004), and copula-adjusted metafrontier. The empirical results suggest that copula-adjusted metafrontier could significantly improve the efficiency of financial holding companies based on the data of sample period 2001-2012. On the framework of copula-adjusted metafrontier, the evidence also imply that financial holging companysubsidiary technical efficiency is better than non-financial holding company compared to the framework of Haung et al.(2013) and Battese et al.(2004), the conclusion emphasis that synergy is perhaps one crucial key factor influenced the efficiency estimation. Otherwise, this study appears to support the copula-adjusted metafrontier model is also well-adjusted compared to programming techniques because not only it enables the statistical inferences to be drawn, but also provides more efficiency estimations.