在這篇論文中，我們將利用值分佈的理論來探討下列函數方程解的存在性與其性質： \[\sum_{j=1}^pa_j(z)f_j(z)^{k_j}=1,\] 其中 $a_1(z),\cdots ,a_p(z)$ 為半純函數。對某些特殊方程，除了文獻裡已知的結果外，我們亦提供其它的例子。一般而言，我們探討解存在的必要條件。另外，我們證明了某一類半純函數之零點與極點之分佈的結果。 / In this thesis, we use the theory of value distribution to study the existence of solution of the following functional equation: \[\sum_{j=1}^pa_j(z)f_j(z)^{k_j}=1,\] where $a_1(z),\cdots ,a_p(z)$ are meromorphic functions. For some special case, new and old examples of the solutions are given. For the general case, a necessary condition for the existence of solution is considered. Moreover, we obtain a result on the distribution of zeros and poles of a class of meromorphic functions.

本篇研究旨在探討利率政策對所得分佈不均的關係，利用 Azzimonti, De Francisco, and Quadrini (2014) 的模型加以延伸擴展，並加入土地或資產的價格變動，從而進一步探討中央銀行的低利率政策對企業主與受薪階層的影響。 模型假設簡單將市場參與者分成2大類，分別是企業家與受薪的勞工，藉由此2大類分別的終生效用函數對利率的變動來說明利率政策對所得分配的影響。Joseph E. Stiglitz (2015b) 提及在低利率政策之下將導致信用的膨脹，進而使土地或資產的價值提高，而土地或資產之價格不斷上漲為造成所得分佈不均之重要原因之一，故本篇論文將土地價格變動納入模型加以延伸，並觀察台灣近幾年之現況。 此篇研究發現，在中央銀行的低利率政策之下，有產階層的企業家之財富條件將會愈來愈好，而與之相對的受薪階層的勞工之財富條件將會愈來愈差；而台灣近幾年之數據亦顯示當利率降低之際，代表所得分佈不均的GINI指數隨之上升，與本篇之研究結果相符。 / The objective of this thesis is to testify the relation between interest rate policy and income inequality. We develop a model based on Azzimonti, De Francisco, and Quadrini (2014) and expand the model by considering the change of the land or asset price so as to analyze the impact of low interest rate on the welfare of entrepreneurs and workers, respectively. The model simply divides the agents into two groups, entrepreneurs and workers, and uses their lifetime utility to explain the impact of interest rate policy on income inequality. Joseph E. Stiglitz (2015b) mentioned that low interest rate would expand the credit availability and drive up the land or asset price. The continuous upward trend of land or asset price is one of the important reason causing income inequality. After taking into account the land or asset price on the sensibility of income inequality toward interest rate, this thesis is able to provide a theoretical underpinning of Taiwan’s empirical observation in recent years. We find out that with low interest rate policy, entrepreneurs’ wealth condition is doing better and better while the workers’ wealth is getting worse. Taiwan’s data in the recent years also shows that once the central bank lowering the interest rate GINI index, which represent the income inequality distribution, will rise immediately. This situation is in accord with the thesis.

產業與都市兩者共生共榮的關係及其相互影響所帶來的效應，是都市計畫學者致力於探討的問題。本研究選擇台北都會區為研究對象，試圖結合產業區位與都會區發展，瞭解各產業分佈與都會區發展過程之關係，並找出足以影響產業進駐之地方性因素，以留住地方產業。首先，本研究分析台北都會區產業結構及重要性，同時利用產業空間分佈圖及區域經濟分析法瞭解各產業於都會區內之空間分佈及變遷情形；最後根據相關理論，找出替代變數探討影響台北都會區二、三級產業之空間分佈及變遷因素，以供未來都市及產業政策之規劃實施之參考。獲致結論如下： 一、台北都會區符合核心－外圍理論所言，其發展過程乃由首要中心一枝獨秀，人口、商業與資源愈趨集中的階段，過渡至分散化的發展開始產生。此外，台北都會區目前正處於都會區生命週期的第二階段－郊區化階段，並出現Norton(1979)所謂集中與分散同時產生的「集中式分散」現象，此將有助於均衡區域發展之目的。 二、從產業的角度來看，本研究發現製造業於台北都會區的成長已逐漸緩慢，整體分佈狀態並無很大的改變，而產業本身的聚集經濟力量及政府工業區計畫情形，以及勞動力的分佈、交流道的設置等則皆為影響製造業區位選擇之因素。三級產業方面，其符合下濾理論及產業生命週期理論，初期興起於繁榮地區，待該區逐漸飽和後則往外部地區擴張移動。而實證結果則得出地區期初之三級產業工資水準、總人口數、產業雜異程度、高等教育人口比例、商業區編定面積及交流道可及性等因素對各類三級產業之分佈皆有顯著影響。 三、從地區性影響因素來看，本研究實證結果發現中人口分佈與產業分佈有顯著正向關係，進一步印證過去研究有關"Jobs follow people"的結論；此外，本研究實證結果證實交流道（高速公路）之開發建設確實對地區產業的發展有顯著的貢獻，同時亦發現一地區專業人才的培養確實有助於吸引產業之進駐。

本研究以探討高雄都會區產業型態與其空間分佈為目的，首先界定研究地理範圍與產業範圍，且對產業型態與空間分佈的分析方法及其相關研究作一番介紹，並以此對高雄都會區的產業型態、產業結構及空間分佈情形作一通盤性探討。 　　本研究內容係以區位商數分析高雄都會區基礎性產業；以CES生產函數探討高雄都會區產業型態；以產業百分比、地方化係數、產業雜異化指標來探討高雄都會區產業結構及其空間分佈；以因子分析法來探討高雄都會區產業活動影響因素；最後以群落分析來劃分高雄都會區產業整體活動、工業活動、服務業活動等中心階層。 　　本研究結果為高雄都會區基礎性產業計有木竹製品業等廿七類，而該等產業經濟型態主要為地方化經濟型態；高雄都會區產業結構以工業為主，但服務業活動已佔了相當大比重；高雄都會區產業活動主要集中於高雄市區，高雄都會區產業發展極不均衡；高雄都會區整體產業活動中心階層以楠梓區、三民區、前鎮區為主要活動中心，高雄都會區工業活動主要分佈在高雄市外緣區域如楠梓區、前鎮區、小港區，而服務業活動主要分佈於高雄市中心區域如三民區、新興區、前金區等。

在這篇論文裡，我們探討 $\mathcal{A}$ 類半純函數的值分佈基本理論。我們證明了每一個 $\mathcal{A}$ 類半純函數最多有兩個重值，而這個結果是最佳的情形。進而，我們證明若一個 $\mathcal{A}$ 類半純函數 $f$ 與其導數 $f^{(k)}$ 共非零的複數值，則 $f\equiv f^{(k)}$。 / In this thesis, we study the basic theory of value distribution of meromorphic function of class $\mathcal{A}$. We prove that every meromorphic function of class $\mathcal{A}$ has at most two multiple values and the result is sharp. Also, we prove that if a meromorphic function $f$ of class $\mathcal{A}$ and its derivative $f^{(k)}$ share a non-zero complex value, then $f\equiv f^{(k)}$.

國民旅遊卡冀望帶動全民非假日旅遊風潮，提振國內觀光旅遊產業景氣，解決結構性及中高齡失業問題，促進區域平衡，使全民受惠，結合公務人員強制休假補助制度，鼓勵從事觀光休閒旅遊活動，紓解工作壓力，樽節國庫開支，改善政府財政負擔。國民旅遊卡施行迄今已屆滿七年，其間經過不斷地修正，所衍生問題是否獲得解決，消費限制措施之必要性，政策目標是否已達成，值得再進一步的探討，引發本研究的動機。 目前國內國民旅遊卡相關研究，多以單一年度同一縣市內特定公務機關或背景身分者進行研究分析，並以滿意度、持用態度與對旅遊之影響及政策執行與問題等面向探討為主，本研究擬以跨縣市不同公務機關、公營事業、各級學校所屬公務人員為對象，並以97及98年度使用國民旅遊卡的歷史經驗，分析其旅遊行為、空間分佈、滿意與認知程度，提出建議供政府主管機關作為改進強制休假補助措施，同時提供旅遊相關業者作為提升經營效益參考依據。本研究方法為問卷調查法，回收有效問卷計518份。 經本研究實證分析結果發現： 在旅遊行為方面，從事國內旅遊的資訊來源為「網路資訊」，選擇旅遊地點的理由為「喜愛旅遊地點」，旅遊動機為「增進親子或家人關係」，旅遊種類為「自然景觀活動」，旅遊方式為「自行規劃」，使用交通工具為「汽車」之比例最高。休假次數集中在「一次」及「二次」，平均休假日數分別為4.05日及4.17日，「工作忙不易排休」的比例仍高，強制休假制度不易落實，另就消費項目來看，選擇「購物」及「餐飲」的比例高於「旅遊/住宿」，對於結合國民旅遊卡鼓勵公務人員從事休閒旅遊活動的效果有限。 就空間分佈而言，北部地區的「台北市」、「台北縣」、「宜蘭縣」，中部地區的「台中市」、「台中縣」、「南投縣」，南部地區的「屏東縣」、「高雄市」及東部地區的「花蓮縣」、「台東縣」為前十個旅遊縣市，然而看似平均分佈的旅遊地點，仍可發現公務機關數較多的台北縣市、台中縣市等都會地區公務人員，選擇以鄰近縣市旅遊為主，其他縣市為輔，隨著異地隔夜限制規定的放寬與取消，選擇就近旅遊的情形將更加明顯，對於冀望藉由國民旅遊卡帶動地方經濟發展，縮短城鄉差距的政策目標顯有落差。 對於國民旅遊卡的滿意與認知程度問卷結果均呈現中間選項，凸顯公務人員對該政策的冷淡反應及消極面對心態，且多利用短期休假將補助額度用完，對觀光旅遊產業的挹注僅止於休假補助費的移轉，加上政府積極開放陸客觀光旅遊的態度，國民旅遊卡對於刺激經濟發展、提振觀光旅遊產業的政策意義顯已不高。 關鍵字：國民旅遊卡、旅遊行為、空間分佈、滿意度、認知程度 / The purpose of National Travel Card is to promote the trend of weekday travel and to enhance domestic tourism industry, which could solve issues of structural and middle-aged unemployment and benefit citizens by facilitating regional balance. Other purposes include encouraging public servants to travel during their compulsory vacations, reducing national expenses, and alleviating fiscal burden. National Travel Card has been implemented for seven years, during which derivative problems have been continuously amended. However, it is imperative to investigate the necessity of consumption restrictions and whether the goals of policy have been achieved. Current studies on National Travel Card mostly focus on single year, specific public institutions in the same city/county, or personal backgrounds; issues covered in these studies are often concentrated on the influence of user attitudes on their travelling behaviors and issues of policy implementation. By contrast, this study investigates civil servants, public enterprises, and schools as subjects, and refers to the usage history of National Travel Card in 2008 and 2009 to analyze users’ tourism behaviors, spatial distribution, satisfaction and cognition. This study then proposes suggestions for government authorities to improve the compulsory vacation system and simultaneously provides tourism business operators with business efficacy guidelines. Questionnaire survey is conducted, and 518 valid samples are collected. Empirical research findings suggest that: With respect to travelling behaviors, the main source of domestic tourist information is “online information”; the main reason for selecting a particular tour location is “fond of the tour location”; the primary motive for travelling is “to foster parent-child relations and maintain ties with family”; the most common travelling mode is “self-planning”; the most frequently used mode of transportation is “automobiles”. Frequency of vacation is around “once” or “twice.” The average vacation days are respectively 4.05 and 4.17 days. A high percentage of respondents reported that “they are busy working and cannot afford to take time off,” indicating that compulsory vacation leave is not easy to be put into practice. In terms of consumer items, more respondents choose “shopping” and “dining” rather than “travelling/accommodation.” Therefore, National Travel Card has limited effects on encouraging civil servants to participate in travelling activities. With regards to spatial distribution, the top ten popular tourist cities are Taipei City, Taipei County, Yilan County, Taichung City, Taichung County, Nantou City, Pingtung County, Kaohsiung City, Hualien County, and Taitung County. Under this seemingly evenly distributed location, it is found that civil servants of Taipei and Taichung prefer to travel around their neighboring cities over other cities/counties. As restrictions of travelling loosen, the pattern of travelling to neighboring cities will be more obvious. Hence, the policy goal that orients at minimizing the rural-city gap and promoting local economy by implementing National Travel Card is not particularly successful. Respondents reported moderate satisfaction and cognition of National Travel Card, revealing civil servants’ indifferent and passive attitudes toward the policy. In addition, they often use short-term vacation to use up the subsidy quota; as a result, the support for tourism industries is limited to the subsidy quota. Furthermore, since the government is now more open to Chinese tourists, the policy that orients National Travel Card to stimulate economic development and tourism industries is not promising. Keywords: National Travel Card, travelling behaviors, spatial distribution, degree of satisfaction, degree of cognition

Simth and Sedransk(1982)採用雙相抽樣的技術推估魚群年齡層的分布，並且在總成本給定的情形下，尋求使事後之前期望損失函數最小的一組最適第二相樣本數。由於期望損失函數過於複雜，而不易於計算處理，所以，他們考慮了一個較為簡單的近似事後之前期望損失函數，由此導出了近似的最適第二相樣本數之公式解。其後Jinn, Sedransk and Simth(1987)繼續探討選取最適第一相樣本數的問題。由於過程中的運算龐大複雜而無法導出公式解，因此Jinn, Sedransk and Simth便提出了近似法和電腦模擬法來解決最適第一相樣本數選取的問題。近似法中仍須使用程序曲折龐雜的演算法以求解，而電腦模擬法則更是必須先執行多次繁複的模擬抽樣後，再以演算法求解；雖然以此所得的解較為精準，但步驟仍難脫於繁瑣複雜。本文中，我們分別就給定各層抽樣率和比例抽樣的情況下，提出了如何藉由簡易的計算便可求得第一相樣本數粗估值的方法。

死亡壓縮(Mortality Compression)意指死亡年齡更集中，是最近廣受注意的研究議題，和生存曲線矩形化（Rectangularization）關係密切，以統計分佈的角度描述，則是死亡年齡會逐漸退化到某個特定年齡。換言之，如果死亡壓縮和壽命有上限兩者都成立，以統計術語而言，代表壽命的期望值有上限、變異數會收斂，可藉由死亡年齡分配探討壽命變化。 本文希望以統計方法與資料品質等兩個面向探討死亡壓縮與延壽之間的關係。除了過去使用的無母數方法，如檢視各年度生命表上死亡分佈的最短區間（25%、50%及75%）與死亡人數最多的年齡（Modal Age）的變化，探討死亡壓縮與壽命是否有延長；另一方面，也將對死亡曲線作參數設定，觀察死亡年齡分佈的標準差變化。由於過往的研究多使用的生命表資料，本研究將比較使用生命表資料（死亡資料經過修勻）或原始死亡人數資料對結果的影響。 本研究藉由電腦模擬比較各種估計標準差方法的差異，包括Kannisto (2000) 提出的SD(M+)法與本文考量的非線性極值法(Nonlinear-Maximization)，衡量何者具有較小的均方誤差，並探討錯誤設定分配偵誤的敏感度；另外，本文可討論使用經過修勻的死亡率及原始死亡率對於估計結果的影響。除了電腦模擬，本研究也套入實際死亡資料（如臺灣、美國、…等國資料，資料來源：Human Mortality Database），檢視死亡壓縮是否存在。 / Mortality compression is one of the popular research issues in longevity risk. It means that the age-at-death would concentrate on a narrower range, and it is also related to the concept of rectangularization of survival curve. In terms of statistical distribution, mortality compression indicates that the age-at-death degenerates to a certain age, and it can be used to study changes of lifespan. If the lifespan has a limit, or mortality compression does exist, this suggests that the life expectancy has a limit and the variance of age-at-death would converge. In the study, we evaluate the mortality compression using the statistical methods and considering the issue of data quality. In addition to the nonparametric methods used in the previous studies, such as shortest confidence interval on the distribution of age-at-death and the modal age, we consider optimization methods for estimating the standard deviation of age-at-death distribution. In specific, we compare the SD(M+) proposed by Kannisto (2000) and the method of Nonlinear-Maximization, and check which method has a smaller MSE (Mean Squared Error). For the issue of data quality, we compare the estimation results of using mortality rates from life table data with those using the raw data. In addition to computer simulation, we consider the sensitivity analysis of age-at-death distribution, to evaluate the estimation method. Furthermore, based on the data from Human Mortality Database, we apply the method of Nonlinear-Maximization to life table data (i.e., graduated mortality rates) and raw data, and check if there are significant differences. The estimation results of empirical study are also used to evaluate if there is mortality compression and if there is a longevity limit.

從民國87年所通過的強制汽車責任保險，可發現我國強制汽車責任險的理賠上限與承保範圍等有了重大的改變，造成汽車任意責任險的計算費率必須要重新估算，然而國內對此方面的文獻探討卻著墨不多，因此學生將會針對任意汽車體傷責任險費率釐算詳細加以探討。 而若要重新估計任意汽車責任險首先要做的工作就是要收集完整正確的損失資料，不過由於損失資料的收集相當困難，因此只能透過模擬的損失資料進行任意責任險的費率釐算。而在有模擬的損失資料情況下我們就可透過損失分佈理論進行下列的分析： (1)透過損失資料的特性推估任意汽車責任險可能之損失分佈為Lognormal 分佈。 (2)透過最大概似估計法與特殊法推估Lognormal分佈之參數，並且採用負對數蓋似函數選擇最佳之估計參數。 (3)透過與強制汽車責任險預期損失與汽車任意體傷責任險預期損失之比例關係，釐算汽車任意體傷責任險之純保費。 (4)建立兩種損失趨勢函數，並透過此兩趨勢函數計算汽車任意體傷責任險之高保額係數。 (5)透過上述步驟之計算結果與現行實施之汽車任意體傷責任險費率作比較，以探討是否現行費率是否有超收或不足的現象。 總之，希望此篇論文能夠對未來的汽車任意責任險之費率釐算與保險司費率監督有所幫助。 / Cause the Legislation Yuan passed the compulsory auto liability insurance bill in 1998, we must have a new actuarial pricing of voluntary auto third party insurance. However, all domestic insurers haven’t revised the rate because the absence of the empirical loss data. In addition, only a fewer researches have focused on the actuarial model of this type of insurance. In this paper, we will investigate the pure premium calculation of the voluntary auto insurance, and outline the appropriate model construction procedures. The data we use are not empirical loss data, we calculate the pure premium by the simulated data. The procedures of this study are summarized in the following: (1) Find the possible loss distribution of voluntary auto third party insurance policy. (2) Estimate the parameters of the loss distribution by the maximum likelihood estimate method and the special method of lognormal distribution. (3) Calculation the pure premium of voluntary auto third party insurance. (4) Calculation the increased limits factor(ILF)by two trend functions, and compare the results of two trend functions. (5) Finally, we examine the gross premiums of the voluntary auto third party insurance and compare our results with the actual voluntary auto liability insurance premiums. Altogether, we hope that this paper could be beneficial to the actuaries and also provide suggestions for the government surveillance.

傳統的保險人在面對保險契約所承保的風險時，常會藉由國際上的再保險市場來分散其保險風險。由於所承保險事件的不確定性，保險人需要謹慎小心評估其保險風險並將承保風險轉移至再保險人。再保險有兩種主要的保險型式，可區分成比例再保契約及超額損失再保契約，保險人將利用這些再保險契約來分散求償給付時的損失，加強保險人本身的財務清償能力。 本研究，主要在於建構未來損失求償幅度或頻率的預測分佈並模擬未來支付求償的損失。簡單重點重複抽樣法是一種從危險參數的驗後分佈中抽樣的抽樣方法。然而，蒙地卡羅模擬是一種利用大量電腦運算計算近似預測分佈的逼近方法。利用被選取危險參數的驗前分佈來模擬其驗後分佈，並建構可能的承保危險參數結構，將基於馬可夫鏈蒙地卡羅理論的吉普生抽樣方法決定最適自留額，同時運用於再保險合約決策擬定過程。 最後，考慮於不同的再保險契約下來衡量再保險人的自負財務風險。基本上我們研究的對象是針對保險人所承保的風險，再藉由上述的方法來模擬、近似以量化所衍生的財務風險。這將有助於保險人清楚地瞭解其承保的風險，並對其承保業務做妥善的財務風險管理。本研究提供保險人具體的模型建構方法並對此建構技巧做詳細說明及實證分析。 / Insurers traditionally transfer their insurance risk through the international reinsurance market. Due to the uncertainty of these insured risks, the primary insurer need to carefully evaluate the insured risk and further transfer these risks to his ceding reinsurers. There are two major types of reinsurance, i.e. pro rata treaty and excess of loss treaty, used in protecting the claim losses. In this article, the predictive distribution of the claim size is constructed to monitor the future claim underwriting losses based on the reinsurance agreement. Simple Importance Resampling (SIR) are employed in sampling the posterior distribution of risk parameters. Then Monte Carlo simulations are used to approximate the predictive distribution. Plausible prior distributions of these risk parameters are chosen in simulation its posterior distribution. Markov chain Monte Carlo (MCMC) method using Gibbs sampling scheme is also performed based on possible parametric structures. Both the pro rata and excess of loss treaties are investigated to quantify the retention risks of the ceding reinsurers. The insurance risks are focused in our model. Through the implemented model and simulation techniques, it is beneficial for the primary insurer in projecting his underwriting risks. The results show a significant advantage and flexibility using this approach in risk management. This article outlines the procedure of building the model. Finally a practical case study is performed for numerical illustrated.