本研究的第一部份是利用有效存續期間與有效凸性來衡量人壽保險人的利率風險。我們發現Tsai (2009)指出的壽險保單準備金之有效存續期間結構並非一般化的結果。當長期利率水準高於保單預定利率及保單解約率敏感於利差時，準備金之有效存續期間會呈現與Tsai (2009)相反的結構。我們進一步發現準備金之有效凸性會亦有可能呈現負值，且不易依照保單到期期限歸納出一般化的結構。負值的有效凸性起因於準備金並非利率的單調函數，且準備金與利率的函數關係隨保單到期期限而不同。我們的研究結果可以幫助人壽保險人執行更為精確的資產負債管理。 本研究的第二部分是利用模擬最佳化的方法，幫助銷售傳統壽險保單的保險人求解出適切的業務槓桿與資產配置策略。我們假設保險人在考量破產機率與報酬率的波動之下，將資本與淨保費收入投資於資本市場中，以追求較高的業主權益報酬率。以業務槓桿與資產配置相互影響為前提，我們求解出適切的業務槓桿與多期資產配置策略，並分析在不同的業務槓桿之下，保險人多期資產配置的差異。 / In the first part of this doctoral dissertation, we focus on a proper measurement on interest rate risk of life insurer’s liabilities, policy reserves, by incorporating the general effective duration and effective convexity measures. Tsai (2009) identified a term structure of the effective durations of life insurance reserves. We find that his results are not general. When the long-run mean of interest rates is higher than the policy crediting rate and the surrender rate is sensitive to the spread, the term structure would exhibit an opposite pattern to the one in Tsai (2009). We further find that the effective convexities might be negative and the term structure of the effective convexities exhibits no general pattern. The irregularities originate from negative effective convexities result from the relationship between mean reserves and initial short rate for different years to maturity. Our results can help life insurers to implement more accurate asset-liability management. In the second part, we analyze asset allocation and leverage strategies for a life insurer selling traditional insurance products by using a simulation optimization method. We assume that an insurer invests equity capital (from its shareholders) and premiums it receives from policyholders by choosing a portfolio intended to maximize the annual return of equity minus the penalty of insolvencies and risks. We regard the leverage as an internal factor in asset allocation. Based on these assumptions, we get a promising multiple-periods asset allocation and leverage, besides analyzing how leverage affects asset allocation strategies.

2008年9月雷曼兄弟突然宣佈破產，使得雷曼兄弟所發行之連動債成為無價值之債券。雷曼兄弟破產事件後讓投資人對於連動債有極大的恐懼，再加上現在全球經濟處於復甦的力道仍有所疑慮的情況，現今發行機構所發行之連動債，都是偏向連結單一商品的連動債，以避免投資人對複雜結構型連動債的恐懼，所以為了讓投資者可以進一步了解市場上所發行的結構型連動債，並且讓發行機構進一步了解其本身之商品，選取了市場上之結構型連動債進行評價與分析。 本篇論文選定之結構型連動債券為｢完全保本黃金連動債券｣，對此商品進行評價與分析。首先介紹商品之特性，此商品為一個付息債券加上一個連結黃金價格之亞式選擇權，由於此商品亞式選擇權的平均部份是算術平均，沒有公式解，所以利用蒙地卡羅模擬法來進行評價與分析，也使用反向變異法和控制變異法來改善傳統蒙地卡羅模擬法收斂速度較慢的缺點，最後結論部分針對商品之設計提出建議。

在生態學、生物學、和比較文學的研究中，物種個數通常是評估生物多樣性的重要指標，單一群落物種數的估計已有非常豐富的相關研究。較為知名者包括Good (1953)提出未出現物種的機率，作為估計物種數的參考，往後Good的想法被大量延伸，推演出不少新的估計方法，像是Burnham and Overton (1978)的Jackknife估計法，Chao and Lee (1992)利用涵蓋機率的估計。相對而言，兩群落共有物種數的研究較少，現有研究中較為知名的有Chao et al. (2000)的估計式。 本研究延伸Good想法，探討Jackknife估計法在兩群落的應用，以出現一次的共有物種（一階Jackknife估計），推估未出現共有物種機率，並且仿造Burnham and Overton的想法，建立共有物種數的估計值及變異數。本文除了以電腦模擬，也使用實例（包括：金庸武俠小說、台灣野生水鳥、巴拿馬螃蟹和巴洛科羅拉多森林）檢驗本文的Jackknife估計法，利用涵蓋機率角度發現抽出某特定比例樣本時，估計值涵蓋母體共有物種數之機率值達到九成以上，且也與Chao提出的估計值比較。 / The number of species is frequently used to measure the biodiversity of a population in ecology, biology, and comparative literature. There are quite a lot of studies related to estimating the number of species. Among these studies, Good (1953) proposed a famous estimate (Turing’s estimate) for the probability of unseen species. Subsequently, many methods have been proposed for estimating the number of species based on Good’s idea. For example, the Jackknife estimator by Burnham and Overton (1978) and sample coverage probability by Chao and Lee (1992) are two famous estimates for the number of species. In contrast, there are not many studies for the number of shared species in two communities, and Chao et al. (2000) is probably the only one. This article extends Good’s idea and the Jackknife method to estimate the number of shared species in two communities. Similar to Burnham and Overton, we establish the estimate and its estimated variance, based on the number of species appearing exactly once. We also use computer simulation and real data sets (Jin-Yong martial arts novels, Taiwan wild birds, Panama crustacean, and Barro Colorado Island forest) to evaluate the proposed method. We found that the coverage probability for confidence interval covering the true number of shared species is more than 90%. In addition, we compare the proposed method with Chao’s method.

一個國家對全國人口有充分瞭解，方能依據國情制定適合的政策，地方發展更是如此，更須洞悉各地的人口結構，以善用有限的資源。台灣近年人口老化日益明顯，各縣市的老化速度及人口問題也不盡相同，若可獲得各地區未來的人口相關數值 (亦即人口推估)，當能減輕未來人口老化對台灣造成的衝擊。本文以縣市層級的人口推估，也就是小區域人口推估為研究目標，探討需注意的事項，尋找適合台灣地區的小區域推估方法。 本文整理小區域人口推估方法，並使用人口要素變動合成法 (Cohort Component Method)，以雲嘉兩縣、臺北市、澎湖縣為範例，測試縣市層級的人口推估。人口推估與生育、死亡、遷移三者的假設有密切關係，我們以死亡率為目標，比較不同模型的優劣，考慮的模型包括 Lee-Carter 模型、區塊拔靴法 (Block Bootstrap)、篩網拔靴法 (Sieve Bootstrap) 以及泛函資料分析 (Functional Data Analysis) 中的主成份分析 (Principle Component Analysis)，以估計誤差為衡量方法優劣的標準。分析發現篩網拔靴法、區塊拔靴法、Lee-Carter 模型三者的結果較佳，因此在小區域推估中使用較簡便的區塊拔靴法。研究發現對小區域的人口推估而言，遷移假設扮演非常重要的角色，此與全國規模的人口推估結果截然不同。研究過程亦發現人口三要素對人口推估有明顯的影響，若假設三要素間互相獨立 (也就是傳統推估時的假設)，推估結果的預測區間遠小於三要素不獨立。 / The government can make policy according to the population change in this country, while the local government can develop their district by using their limited resources well after realizing the populaton structure. The population ageing is becoming more serious and being more different among every counties in Taiwan day by day. If we can get the relative numbers of population in the future (population projection), we can decrease the attack of population ageing for Taiwan. The aim of this paper is to find an appropriate method and some notations of small area population projection in Taiwan. The paper includes the summary of methods of small area population projection and the results by using cohort component method on three areas in Taiwan, YunLin & ChiaYi, Taipein City and PengHu. Population projection is highly related with birth, death and migration, hence we test the mortality rate by using several methods, Lee-Carter, block bootstrap, sieve bootstrap and principal component analysis of functional data analysis are included. We found that the result of sieve bootstrap, block bootstrap and Lee-Carter are much better than the others, therefore, we take block bootstrap which is much simpler than the other two to analysis the effect of birth, death and migration in population projection. The sutdy found that, in small area population projecton, migration plays an important role, which is totally different from the whole country population projection.

本論文的研究目的，主要是希望利用Martingale評價方法與蒙地卡羅模擬法評價出結構型商品條款中隱含的新奇選擇權（Exotic Options）價格，並進而推導出結構型商品的理論價值，並且，期望藉由對個案商品的評價與損益分析，讓讀者瞭解結構型商品的產品結構、報酬型態與成本及潛在風險；此外，本文也從發行券商的角度，探討券商所面臨的潛在風險並提出可行的避險策略。 Martingale評價方法(The Martingale Pricing Method)由Cox與Ross(1976)及Harrison與Kreps(1979)所提出，是一種求解衍生性商品評價的方法，在Martingale評價方法下，衍生性商品的理論價格可經由折現該商品未來期望現金流量而得，且期望值折現可在風險中立環境下進行，折現率使用無風險利率。Martingale評價法在財務工程界是一項沿用已久的數學工具。本論文的主要貢獻，就是延伸Martingale評價法，透過機率測度轉換，推導出多資產股權連動式商品的評價公式解，進而求算出商品的理論價值。 本論文採用在市場上銷售的兩個結構型商品作個案分析，兩個案分別為多資產股權連動式票券與路徑相依指數連動式債券，主要研究成果如下： □ 以Martingale評價法作為本論文的評價模型，採用多資產股權連動式票券為個案，延伸評價模型求出產品的封閉解，並探討此種商品的報酬型態與潛在風險。 □ 以蒙地卡羅模擬法評價本論文的另一項個案—路徑相依指數連動式債券的理論價值，並分別從投資人與發行商的角度，探討產品的利潤與風險。 □ 在程式應用方面，運用MATLAB軟體，以模擬並求算產品的理論價格。

由於台灣地區的生育率變化較大，之前的研究發現其他各國的生育率模型不見得適用，亟需建立可反映我國國情的生育率模型。本文引用台灣、日本、荷蘭、美國（亞洲、歐洲、美洲）等經濟發達國家的出生資料，配適包括Gamma、Lee-Carter、主成份分析、年齡組個別估計法、擴散模型等較為常用的模型，比較這些國家配適結果的異同。分析發現，如果要預測總生育率，台灣、日本、美國都是以年齡組生育率個別配適擴散模型的結果最佳，荷蘭則是年齡組個別估計法；在年齡組生育率的預測方面，台灣、日本、荷蘭都是以年齡組生育率個別配適擴散模型最好，美國則是以年齡組個別估計最好。此外再從相對穩定性或相對效率的角度來評判，一樣是以年齡組生育率個別配適擴散模型或年齡組個別估計的總生育率預測結果最佳。最後還觀察到台灣地區和各縣市的有偶婦女比例和生育率呈正向關係，平均生育年齡和生育率呈反向關係，各縣市在有偶婦女比例、生育率、平均生育年齡的變化並不一致，各年齡組有偶婦女比例和生育率的改變也不盡相同。

在觀察性研究或非隨機試驗研究中，欲探討因果效應時，研究者需要重新對觀察性研究進行設計，設計目的在於重新建立一個隨機指派受試者的機制，使其得以近似一個隨機試驗研究，這樣的研究一般稱為「類隨機試驗研究」(quasi-randomized-experiments)。 傾向分數分析即為一種設計觀察性研究的方法，在不牽涉到反應變數結果之下進行設計。本文於一個病例對照研究(case-control study)中使用傾向分數進行配對接著再進一步估計處理效果，傾向分數配對是可降低觀察性研究中的選擇性偏誤的方法，透過配對可減少實驗組與對照組間的系統性差異，使研究群體在所觀察到的控制變數分配達到相似，進而得到處理效果(treatment effect)的不偏估計，為近年廣受流行病學、經濟學以及社會學領域使用的方法之一。傾向分數本身為一個條件機率，定義為研究受試者在其所觀察到的控制變數之下，接受某處理或被指派至某特定群體的機率，估計傾向分數最常見的方法為羅吉斯迴歸。 此外，自1970年代起，配對方法(matching method)開始被使用來選取合適的實驗組與對照組並進行兩群體的比較，其中「確切配對」屬於最常使用的配對方法，過去文獻中經常可見各種配對方法的結合使用，因此，本文電腦模擬研究部份，欲比較四種情境之下「傾向分數配對」與「確切配對」結合使用的效果，分別以偏誤降低比例、信賴區間覆蓋率、均方誤衡量兩種配對方法結合使用的適合情境。結果顯示若對「與處理指派中度相關的變數」且「與反應變數高度相關的變數」，其效果最為明顯。根據結果，我們總結認為「確切配對與傾向分數配對合併使用」確實會有較好的表現，但表現的好壞也取決於確切配對的變數。實證研究部份，探討家庭結構對青少年偏差行為之影響，欲了解來自非完整家庭之青少年是否較來自完整家庭之青少年更有容易出現偏差行為。 / In observational or nonrandomized studies, treatments are not randomly assigned so that baseline differences between treated and control groups are typically observed. Without properly executed, the differences would bias the treatment effect estimates. There has been a long history of using matching to eliminate confounder bias, and inferences are made based on the matched observations. The theoretical basis for matching has been developed since 1970, and among those matching methods commonly in use, the exact matching is probably the most popular one. On the other hand, introduced by Rosenbuam and Rubin in 1983, propensity scores, the conditional probability of being exposed or treated given the observed covariates, has been a welcome alternative used to adjust for baseline differences between study groups of late. Instead of matching a treated with an untreated subject by their covariates, subjects in both treated and control groups are matched by their propensity scores. In this study, we explore the benefits of using propensity score matching together with the exact matching for adjusting for baseline differences through Monte Carlo simulations. An empirical study is also be provided for illustration.

在因子模型下，損失分配函數的估算取決於混合型聯合違約分配。蒙地卡羅是一個經常使用的計算工具。然而，一般蒙地卡羅模擬是一個不具有效率的方法，特別是在稀有事件與複雜的債務違約模型的情形下，因此，找尋可以增進效率的方法變成了一件迫切的事。 對於這樣的問題，重點採樣法似乎是一個可以採用且吸引人的方法。透過改變抽樣的機率測度，重點採樣法使估計量變得更有效率，尤其是針對相對複雜的模型。因此，我們將應用重點採樣法來估計偏常態關聯結構模型的尾部機率。這篇論文包含兩個部分。Ⅰ：應用指數扭轉法---一個經常使用且為較佳的終點採樣技巧---於條件機率。然而，這樣的程序無法確保所得的估計量有足夠的變異縮減。此結果指出，對於因子在選擇重點採樣上，我們需要更進一步的考慮。Ⅱ：進一步應用重點採樣法於因子；在這樣的問題上，已經有相當多的方法在文獻中被提出。在這些文獻中，重點採樣的方法可大略區分成兩種策略。第一種策略主要在選擇一個最好的位移。最佳的位移值可透過操作不同的估計法來求得，這樣的策略出現在Glasserman等(1999)或Glasserman與Li (2005)。 第二種策略則如同在Capriotti (2008)中的一樣，則是考慮擁有許多參數的因子密度函數作為重點採樣的候選分配。透過解出非線性優化問題，就可確立一個未受限於位移的重點採樣分配。不過，這樣的方法在尋找最佳的參數當中，很容易引起另一個效率上的問題。為了要讓此法有效率，就必須在使用此法前，對參數的穩健估計上，投入更多的工作，這將造成問題更行複雜。 本文中，我們說明了另一種簡單且具有彈性的策略。這裡，我們所提的演算法不受限在如同Gaussian模型下決定最佳位移的作法，也不受限於因子分配函數參數的估計。透過Chiang, Yueh與Hsie (2007)文章中的主要概念，我們提供了重點採樣密度函數一個合理的推估並且找出了一個不同於使用隨機近似的演算法來加速模擬的進行。 最後，我們提供了一些單因子的理論的證明。對於多因子模型，我們也因此有了一個較有效率的估計演算法。我們利用一些數值結果來凸顯此法在效率上，是遠優於蒙地卡羅模擬。 / Under a factor model, computation of the loss density function relies on the estimates of some mixture of the joint default probability and joint survival probability. Monte Carlo simulation is among the most widely used computational tools in such estimation. Nevertheless, general Monte Carlo simulation is an ineffective simulation approach, in particular for rare event aspect and complex dependence between defaults of multiple obligors. So a method to increase efficiency of estimation is necessary. Importance sampling (IS) seems to be an attractive method to address this problem. Changing the measure of probabilities, IS makes an estimator to be efficient especially for complicated model. Therefore, we consider IS for estimation of tail probability of skew normal copula model. This paper consists of two parts. First, we apply exponential twist, a usual and better IS technique, to conditional probabilities and the factors. However, this procedure does not always guarantee enough variance reduction. Such result indicates the further consideration of choosing IS factor density. Faced with this problem, a variety of approaches has recently been proposed in the literature ( Capriotti 2008, Glasserman et al 1999, Glasserman and Li 2005). The better choices of IS density can be roughly classified into two kinds of strategies. The first strategy depends on choosing optimal shift. The optimal drift is decided by using different approximation methods. Such strategy is shown in Glasserman et al 1999, or Glasserman and Li 2005. The second strategy, as shown in Capriotti (2008), considers a family of factor probability densities which depend on a set of real parameters. By formulating in terms of a nonlinear optimization problem, IS density which is not limited the determination of drift is then determinate. The method that searches for the optimal parameters, however, incurs another efficiency problem. To keep the method efficient, particular care for robust parameters estimation needs to be taken in preliminary Monte Carlo simulation. This leads method to be more complicated. In this paper, we describe an alternative strategy that is straightforward and flexible enough to be applied in Monte Carlo setting. Indeed, our algorithm is not limited to the determination of optimal drift in Gaussian copula model, nor estimation of parameters of factor density. To exploit the similar concept developed for basket default swap valuation in Chiang, Yueh, and Hsie (2007), we provide a reasonable guess of the optimal sampling density and then establish a way different from stochastic approximation to speed up simulation. Finally, we provide theoretical support for single factor model and take this approach a step further to multifactor case. So we have a rough but fast approximation that execute entirely with Monte Carlo in general situation. We support our approach by some portfolio examples. Numerical results show that such algorithm is more efficient than general Monte Carlo simulation.

不動產證券化可行性之研究 摘要 為解決傳統不動產投資困境，將不動產投資方式由固定的資產形式轉變為證券型態的概念，而有不動產證券化（Real Estate Securitization）的產生。國內主要的不動產證券化模式分為不動產投資信託（Real Estate Investment Trust）與不動產資產信託（Real Estate Asset Trust），這兩種模式未來市場供需面實際運作的可行性為何，將是不動產證券化制度成功與否的重要關鍵。 本研究先從需求面投資者的角度切入，透過問卷調查資料，運用Logit模型探討證券化可行性因素對於投資者購買不動產受益證券的影響。實證結果發現，一般投資者認為受益證券的市場流通性、分散風險的重要性愈高，以及預期報酬率愈高，其購買不動產受益證券的可能性愈高；在總體因素方面，對於未來證券市場情況愈樂觀，以及房地產市場情況愈樂觀，其購買受益證券的機率將愈高；法人投資者則認為分散風險的重要性愈高，以及該法人機構主要投資工具的種類愈多，其購買不動產受益證券的機率愈大。 以供給面不動產持有者財務上的可行性而言，其財務目標在追求自身的ROE極大化，因此不動產持有者將視各項風險來源對於投資報酬的影響，決定是否運用證券化投資方式。模擬分析結果發現，除了不動產持有者本身的財務結構限制與不動產經營能力之外，在個別考量委託成本風險與開發風險的情況下，其對於不動產持有者ROE的影響較小，但營運風險相較於其他風險來源，對於不動產持有者ROE的影響較大；綜合各項風險來源同時納入考量時，發現不動產持有者自有資金比例愈低，其運用證券化方式的ROE較高，但變動的幅度也較大。此一實證與模擬分析結果，對於未來國內不動產證券化實際運作，可提供政府、業者及一般投資大眾作為決策參考。 關鍵字：不動產證券化、不動產投資信託、不動產資產信託、Logit模型、蒙地卡羅模擬 / A Feasibility Study of Real Estate Securitization in Taiwai Abstract By transforming real assets into securities , real estate securitization is created to solve the liquidity problem of real estate investment. The real estate securitization system in Taiwan is divided into two types - Real Estate Investment Trust and Real Estate Asset Trust. Whether the real estate securitization system succeeds or not is based on the feasibility of the market operation in practice. On the demand side, this research uses Logit model to analyze the impact of the feasibility of the real estate securitization system on the investors’ behavior of buying beneficiary certificates by sampling from intuitional investors and individual investors. The empirical results show that the individual investors emphasize on liquidity, divergence, and expected return. In addition, the probability of buying real estate beneficiary certificates increases with the degree of their optimistic expectation on both the stock and the real estate markets. However, the institutional investors regard the divergence of portfolios and investment instruments as the main factors of their buying those certificates. On the supply side, given the financial objective of ROE maximum, the owners of the real estate will review all of impacts of risk on return of investment before their decision to take the way of securitization. In addition to the financial structure and the management ability of the owners, the results of Monte Carlo simulation on the effect of real estate securitization also reveal that: a. There is little influence on the ROE of the owners’ real assets while taking trust cost risk and land development cost risk into consideration. b. The influence of operation risk on ROE is more than that of other risks. c. Lower the proportion of capital, higher the ROE and bigger the variation of the ROE are. The results of empirical analysis can be a reference of decision making for Government, trust industry, and investors in the real estate security market operation. Keywords：Real Estate Securitization , Real Estate Investment Trust , Real Estate Asset Trust , Logit Model , Monte Carlo Simulation

影響海外可轉換公司債的因素有許多，包括股價、國內利率、國外利率、匯率，若將時間變數也加入計算，其變動因子高達5階，這種「高維度」的問題已非有限差分法或樹狀方法能處理；且海外可轉債常附有平均式條款、回顧式條款等「路徑相依」性質的選擇權，更是格狀結構數值法(Lattice)難以處理的問題。若使用蒙地卡羅模擬，雖然可以處理高維度及路徑相依的問題，但遇到美式契約時，則會有無法判斷轉換時點的問題，更遑論還必須處理的重設條款或界限型契約。 本論文研究海外可轉換公司債的評價，特點是可以處理其契約中各種可能的複雜條款，本文所使用的最小平方蒙地卡羅模擬，由Longstaff and Schwartz [2000]提出，對於美式契約、路徑相依及高維度問題皆可處理。本文並以Hull and White利率三元樹配適公司債利率符合市場利率期間結構。此外本研究加入海外可轉換公司債評價中最重要的信用風險因素，過去可轉債文獻理論價格大都高於實際市價，這是由於忽略了公司的信用風險溢酬，本文所使用的信用風險模型是由Lando [1998]所提出，特點是不以信用等級作為考量，探討公司特性與所屬產業，並考慮總體因素對違約機率的影響，從市場價格中估計違約密度參數，進而求得信用價差。 本研究對仁寶電腦在2002年所發的ECB做實證研究，比較LSM理論價格與實際市價之誤差，及對Takahashi[2001]所提出之歐式模型做比較，發現本文提出模型之評價結果相當不錯，誤差僅有0.83%；此外並對建華金控2002所發之ECB，探討各種複雜新奇條款對ECB價格的影響，發現市場上嚴重低估了重設條款所提高的價值，而實際市價卻十分接近僅含賣回條款的理論價格。