台灣信用卡市場自1982年全面開放以來，信用卡以驚人的速度不斷成長。但隨著信用卡簽帳金額、循環信用餘額的提高，以及2002年南韓信用卡泡沫危機的前車之鑑，信用卡逾期放款的風險控制也逐漸為政府相關主管機關所注意。藉由2003年7月至2004年10月，共16個月的月資料以及43間發卡機構，作追蹤資料的隨機效果模型分析，並採三種方向作為研究的角度，顯示較低逾放比的銀行，也許其風險管理及內部控制較為嚴謹，因此其信用卡部門之逾放情形也會較少。益本比則可以反映獲利能力較佳之銀行其放款品質較佳，因此可以推估其信用卡逾期放款的情形相對而言較不嚴重。持卡人循環信用餘額使用指數則反映出貸款者的還款能力。卡均循環信用餘額則是一項較為特殊的觀點。結果顯示台灣確發生了以卡養卡的情形，以致於在短期內，卡均循環信用餘額的提高反而會造成信用卡逾放比率的改善。最後，景氣動向指標成長率則反映出在景氣好的時候，持卡人比較有意願及能力償還其信用債款，因此持卡人逾期繳款的情形較不會發生。

本文研究目的是在探討跨國的投資者在面對國際投資日益開放的同時，是否充分的利用國際上的資產市場以分散投資者所面對的風險。本文參考Brandt, Cochrane, and Santa-Clara（2006），建立一種衡量國際間風險分散程度的風險分散指數，並以台灣為本國基準，取台灣前三大貿易夥伴：美國、日本、中國為外國基準，以分析此四國的國際風險分散指數，衡量的標的為各國資產市場中的主要股票交易市場指數報酬率，以分析各國風險分散的情形。此外我們亦嘗試解釋國際間風險分散的情形並解釋我們所計算出的結果，並進行一些模型參數的演算，以分析在面對其他總體變化時將會遇到的情形。經由本文的實證研究發現，對於台灣而言，在國際間的風險分散程度是偏高的，亦即，面對此四國的資產市場，台灣投資者的投資配置符合風險分散的趨勢，當匯率波動愈小時，國際風險分散程度亦將愈高，大致上與Brandt et al.(2006)之以美國為本國基準所得之國際風險分散程度結果相似。 / This thesis tries to discuss if risks are shared internationally by the international asset markets. This study refers to the Brandt, Cochrane, and Santa-Clara (2006) which built an international risk sharing index to measure the degree of international risk sharing. We set up a international risk sharing indices between Taiwan and its important trading partners, US, Japan and China by the asset returns composed by the main stock indices in each country. Furthermore, we try to explain the empirical results and to show how the degree of international risk sharing will different with the changes of the macro-variables. Our empirical analyses find that the degree of the international risk sharing for Taiwan using asset-based method is better than we think. In addition, the empirical results of this thesis are similar to Brandt et al. (2006) that if the volatility of exchange rates declines, the degree of the international risk sharing will be better.

當保險契約被發行時，保險公司必須被要求盡可能的具備承擔未來不可知的風險的能力。本文將死亡風險、利率風險、脫退風險以及流動性風險引入，並針對生死合險契約進行盈餘分析。在此以 Vasicek (1977) 所提出之隨機利率模型、根據被保險人理性行為作為基礎之脫退模型以及引入簡化後的 Longstaff、Mithal與Nies (2005)流動性風險債券價格來描述各種風險。根據上述模型假設下計算保費及準備金，遂以蒙地卡羅模擬法量化源於各種風險之盈餘。最後，本文計算保險公司之盈餘對各風險參數之敏感度分析，並計算各期破產與發生流動性問題之可能性。 / Once insurance contracts are issued, the insurers should be capable to deal with the unknown conditions in the future as possible. In this paper, we analyze the impact of mortality, interest rate, surrender and liquidity risks on the surplus of endowment contract. We model the interest rate risk by Vasicek model, the surrender rate based on the rational behavior of policyholders and introduce the discounted price of zero coupon bonds as the liquidity risk. Under such assumptions, we compute the premium and reserve, demonstrate the simulated insurance surplus, and finally exhibit the statistics of the surplus from different sources. The simulated results show the sensitivity of the surplus to the parameters of the risks. At the same time, we also show the probabilities of insolvency and illiquidity of the insurer before the maturity date of the contract due to the fluctuating surrender rate and liquidity risk resulting from the stochastic interest rate.

此研究主要研究壽險業的系統性風險與違約風險之評價，基於投資組合的波動度去建立隨機過程模型。特別是那些隱含無法被多角化的財務風險、系統性風險，透過研究，使用Heston(1993)模型去描述標的資產的隨機波動程度比以往使用Black-Scholes(1973)模型描述股價的波動變化更能反映實際的風險狀況，並透過CIR過程來表示瞬間的波動程度。在這個模型之中，把過去以平賭測度決定違約選擇權的方法延伸。此外透過探討違約價值之敏感度，根據不同的情境測試對於壽險公司負債的影響。最後透過數值的結果與敏感度分析隨機波動模型與確定性的模型之差異。 當資本準備增加時，資產與負債比提高，因負債仍固定承諾予保戶之利率增長，而資產因應系統性風險的發生而減損仍能支付負債，致使違約風險降低，進而使得評價時點的違約金額降低。當系統風險發生時，風險值上升，違約價值為右偏分布，代表在極端條件下有可能有極大的損失；反之，當整個金融體系經濟情勢良好，公司擁有足夠的經濟資本時，風險值下降，滿足VaR75與CTE65的法規限制，此時公司的清償能力足以反映系統性風險。 / This paper considers the problem of valuating the default option of the life insurers that are subject to systematic financial risk in the sense that the volatility of the investment portfolio is modeled through stochastic processes. In particular, this implies that the financial risk cannot be eliminated through diversifying the asset portfolio. In our work, Heston (1993) model is employed in describing the evolution of the volatility of an underlying asset, while the instantaneous variance is a CIR process. Within this model, we study a general set of equivalent martingale measures, and determine the default option by applying these measures. In addition, we investigate the sensitivity of the default values given regulatory forbearance for the life insurance liabilities considered. Numerical examples are included, and the use of the stochastic volatility model is compared with deterministic models. As reserve of capital is increasing, asset-liability ratio is also increasing. The liability grew up with promised interest rate, and it could be covered by the asset when the systematic risk events happened. Therefore, the default risk was decreasing, that caused the default value decreasing. When the systematic risk events happened, the value of risk was increasing, and the default value was positive skew distribution. That means the maximum loss will be coming in the extreme case. On the other hand, when prosperity economy occurred, the value of risk was decreasing, which in compliance with the law of VaR75&CTE65 rules, and the insurance company had enough capital to face the systematic risk events.

未拋補利率平價說的不成立，衍伸出平均報酬大於零的利差交易(carry trades)。 過去基於風險解釋的文獻，提出各種風險因子欲歸因此套利策略的不尋常超額報酬，實為承擔不同風險的額外補償，亦即風險溢酬(risk premium)。 不同的風險因子可略分為兩派：一為有經濟理論根據，卻在實證上未獲支持的「消費成長因子」；二為在實證上具顯著解釋力的「外匯相關因子」， 卻無理論依據而難以賦予利差交易報酬經濟意義。 本文主張以無風險實質利率作為風險因子。此想法源於隨機貼現因子(stochastic discount factor)之定義式以及現實環境中的觀察。 我們的實證發現，實質化的美國公債利率對於利差交易的報酬有顯著的定價能力。 本文更進一步驗證，本因子甚至比起文獻上的外匯波動度因子，更具顯著的定價能力。另外，本因子亦能解釋動能利差交易之報酬，此為高減低因子所不能定價的報酬。

依據「多層次混合試題反應理論」與「隨機試題混合模型」，本研究提出「混合試題與受試者模型」。本研究旨在評估此模型在不同樣本數、不同試題差異功能的試題數下，偵測試題差異功能的表現，以及其參數回復性情形。研究結果顯示，「混合試題與受試者模型」在樣本數大、試題差異功能試題數較多之情境下，具有正確的參數回復性，能正確判斷出試題是否存在試題差異功能，且具有良好的難度估計值，並能將樣本正確地分群，其也與「隨機試題混合模型」的估計表現頗為相近。建議未來可將「混合試題與受試者模型」應用於大型教育資料庫相關研究上，並加入其他變項後進一步探討。 / Drawing upon the framework of the multilevel mixture item response theory model and the random item mixture model, the study attempts to propose one model, called the mixture items and examinees model(MIE model). The purpose of this study was to assess the respective performances of the model on different sample-sizes and differential item functioning (DIF) items. Particularly, the study assessed the model performances in the detection of DIF items, and the accurate parameters recovery. The results of the study revealed that with large sample-sizes and more DIF items, the MIE model had the good parameters recovery, the accurate detection of the DIF items, the good estimate of the item difficulty, and the accurate classifications of the sub-samples. These model performances appeared similar to those of the random item mixture model. The findings suggest that future studies should apply the MIE model to the analyses on large-scale education databases, and should add more variables to the MIE model.

美元在世界上具有獨特的地位，大部份在國際上貿易的商品都以美元做為訂價，Devereux, Shi and Xu (2007)依此情況而把美元稱為國際上的參考貨幣(reference currency)。本文即以美元為參考貨幣的情況，建立一兩國動態隨機一般均衡(Dynamic Stochastic General Equilibrium)模型來探討在世界經濟體系中，有參考貨幣時，貨幣衝擊對兩國經濟體系的影響，以及當面對外在環境衝擊時，兩國政府應該如何選擇適當的貨幣政策。結果發現，擁有參考貨幣的國家發生貨幣衝擊時，對兩國的產出都有正面的影響，然而非參考貨幣國家發生貨幣衝擊時，反而有以鄰為壑(beggar-thy-neighbor)的效果。而在面臨外在環境衝擊時，選擇穩定通貨膨脹的利率法則對兩國而言都會帶來較好的福利效果。 / The U.S. dollars in the world possess a unique position; the majority of the international tradable goods are priced in the U.S. dollars. This paper sets up a two-country DSGE model where the U.S. dollar serves as the reference currency to quantitatively examine the impacts caused by the monetary shocks, as well as how both governments should adopt their monetary policies when facing external shocks. The results show that there are positive impacts on both countries' outputs when a monetary shock occurs in the reference-currency-holding country; Conversely, there is a beggar-thy-neighbor effect when the shock takes place in the other country. In general, the inflation-targeting interest rate rule leads to greater welfare in both countries.

本研究中以隨機模擬的方法應用於退休金最佳控制理論中，並將下跌風險(Downside Risks)加入二次最佳化函數中作為最適化準則，再以英國與美加地區不同提撥率模型做為研究對象，觀察不同情境下之結果。Haberman(1994)首先提出以最適化方法應用於固定給付制退休金基金上，並具體建立二次最適化準則，以提撥與資產的變異作為控制因子。Chang(2003)以下跌風險的觀念，指出退休金基金經營時管理人常較注意提撥過多與資產不足風險，若經營時考慮下跌風險，則會產生與原來考量不同之結果。本文以Chang(2003)之研究為基礎，將其建議之最佳化函數做為考量下跌風險之依據，並提出改良英國與美加地區之提撥率模型，採模擬的方式進行最佳化，探討其對不同提撥率模型之影響。研究結果發現若以隨機模擬作為最佳控制方法，在不同人口假設及精算模型下，會產生相同之結果，且發現下跌風險對於不同提撥率模型有不同之影響，其中建議的英式模型有效降低風險，而美式提撥率模型對於提撥率比例與資產負債比例在最佳化下有較理想之結果。最重要的，退休金基金管理人可利用隨機模擬的方式進行最佳化控制，以提供決策之參考依據。

在運動產業逐漸興起的現代，如何評比球隊或運動員的表現好壞，似乎成了現在新興的熱門話題。經濟學上用來評估一家廠商的生產績效優劣，常用的是生產效率分析，生產活動偏離生產邊界的程度代表不效率高低。而球隊比賽的過程就像廠商生產的過程，運用各種投入得到產出。在籃球比賽中，比賽的投入可為球隊的各種技術統計，例如：投籃命中率、抄截、火鍋…等等，產出則是比賽的得分數。因此，在本篇文章中，我們利用經濟學中的生產效率分析來分析球隊的表現優劣，即評估各球隊發揮其潛能的程度。 評估生產效率的模型有很多，由於比賽的性質，有時候統計誤差、運氣也佔了很重要的部份，所以在選擇模型時，選的是隨機邊界效率分析模型（Stochastic Frontier Approach, SFA），除了利用隨機邊界分析模型分析球隊的生產效率，也利用預估的效率值來預測比賽結果排名，並與一般常用來預測結果的模型PROBIT MODEL做比較。我們利用大陸男子甲A籃球聯賽2003-2004和2004-2005賽季作為實證樣本，發現隨機邊界分析模型不只可以用來評估效率，在預測比賽結果排名上，隨機邊界分析模型預測能力則與PROBIT MODEL沒有顯著統計性的差異。 關鍵字：生產效率、隨機邊界分析法、運動產業 / Today, sports industry is getting popular, and how to evaluate the performance of sports teams or players seems also to be a newly hot interesting topic. In economics, production efficiency is often applied to evaluate a firm’s production performance. The inefficiency of a production activity is measured as its deviation from the production frontier. The process of a sport game is similar to a firm’s production process, which transforming various inputs into output(s). For basketball games, inputs can be the various technical statistics, such as field goal rate, steals, blacks, assistant attack, etc. Output(s) can be the scores of the teams got. Therefore, in this paper we use the production efficiency to gauge the performance of sports teams. There are many models measuring production efficiency. In this paper we choose the Stochastic Frontier Approach (SFA) to evaluate the sport team’s efficiency on account of the white noises which exist in the sport game obviously. We also use estimated efficiency scores to predict the outcome ranking of teams, and compare it to that of the PROBIT MODEL which is usually used to predict the outcome of a game. The sample we used are the results of the CBA men’s regular season and playoff season, and we found that the SFA is not only to evaluate efficiency but also can predict the outcome of competition, and its prediction ability is not significantly statistically different to that of PROBIT MODEL. Keywords: Production Efficiency, Stochastic Frontier Approach, Sports Industry

本論文主要是介紹並評估一個R的軟體套件叫做"rBeta2009"。此套件是由Cheng et al. (2012) [8] 所設計，其目的是用來產生貝他分配(Beta Distribution)及狄氏分配(Dirichlet Distribution)的亂數。本論文特別針對此套件之(i)有效性(effiniency)、(ii)精確性(accuracy)及(iii)隨機性(randomness)進行評估，並與現有的R套件作比較。此外，本論文也介紹如何應用此套件來產生(i)反貝他分配(Inverted Beta Distribution)、(ii)反狄氏分配(Inverted Dirichlet Distribution)、(iii)Liouville分配及(iv)凸面區域上的均勻分配之亂數。 / A package in R called "rBeta2009", originally designed by Cheng et al. (2012) [6], was introduced and evaluated in this thesis. The purpose of the package is generating beta random numbers and Dirichlet random vectors. In this paper, we not only evaluated (i) the efficiency, (ii) the accuracy and (iii) the randomness, but also compare it with other R packages currently in use. In addition, it was also scrutinized in this thesis how to generate (i) inverted beta random numbers, (ii) inverted Dirichlet random vectors, (iii) Liouville random vectors, and (iv) uniform random vectors over convex polyhedron by using the same package.