The author has found, during her experience teaching students on the fourth grade level, that some concepts of number theory haven't even been introduced to the students. Some of these concepts include prime and composite numbers and their applications. Through personal research, the author has found that prime numbers are vital to the understanding of the grade level curriculum. Prime numbers are used to aide in determining divisibility, finding greatest common factors, least common multiples, and common denominators. Through experimentation, classroom examples, and homework, the author has introduced students to prime numbers and their applications.

本論文是由三篇關於金融市場的實證研究組合而成。第一篇以權益存續期間為主題，主要是利用迴歸模型估計台灣上市產業指數的實證權益存續期間，以探討股票報酬率的利率敏感度。迴歸模型中控制了三個重要的股票風險因子─市場因子、規模因子與價值因子。但其中，我們改以正交市場因子代替市場因子，以避免因為利率變動與市場報酬間存在共線性，而造成權益存續期間有可能錯估的問題。此外，基於權益存續期間具有會隨時間改變的動態特性，本文亦對各產業指數最近一次結構性變化的發生時點進行偵測，並據以推估最近期的權益存續期間。實證結果顯示：除了鋼鐵業的權益存續期間不顯著之外，其他所有產業指數皆具有負的權益存續期間，表示其報酬率與利率變動呈現出正向關係。在程度上，則以營建類指的利率敏感度最大，汽車類指最小。 第二篇應用了Diebold and Yilmaz (2009)的外溢指標分析台灣上市產業指數間的連動性，其優點是可以瞭解到產業間相互影響的方向以及程度。實證結果顯示：台灣上市產業指數間的外溢程度頗高，並以營建業為最主要的影響者，而相反地，鋼鐵業則是主要的被影響者。外溢指標具有隨時間改變的動態特性，而且透過動態外溢指標可觀察到次貸風暴蔓延的嚴重性。 第三篇應用了Goyal, Perignon and Villa (2008)所提出的多群組因素分析法，檢測美國總人口死亡率的共同因子個數。該方法最大的優點是能夠有效地辨識出真正的共同因子，避免了一般因素分析容易將解釋能力高的群組內獨特因子誤認為共同因子的缺點。根據檢測結果顯示，美國總人口死亡率的共同因子共有兩個，而且第二個因子的重要性隨時間愈來愈明顯。 / This thesis consists of three empirical essays about financial markets. The first essay analyzes the sensitivity of stock returns to changes in interest rates by estimating empirical equity duration of 18 industrial indices in the Taiwan Stock Exchange. In the regression models, we also control for the market excess return and the Fama-French mimicking returns for size and book-to-market factors. To avoid the effects of the multicolinearity between the market excess return and the interest rate changes, we replace the market excess return by the orthogonalized market factor. In addition, considering the time-varying pattern of empirical equity duration, we further adopt the reversed ordered Cusum test proposed by Pesaran and Timmermann (2002) to identify the most recent break of the regression relationship, and then extract the post-break data to re-estimate the up-to-date empirical equity duration. The result shows that except the Steel index, all industrial indices exhibit significantly negative equity durations, indicating a positive relationship between industrial index returns and interest rate changes in Taiwan. Among them, the Construction index has the largest interest rate sensitivity, while the lowest one is for the Automobile index. The second essay focuses on the nature of financial market interdependence, both in terms of returns and returns volatilities. Being capable of identifying the direction and magnitude of linkages among financial markets, the spillover index proposed by Diebold and Yilmaz (2009) is used to measure return and volatility spillovers between the top eight industrial indices based on market value in the Taiwan Stock Exchange. We find that for both returns and volatilities, the spillover effects among industrial indices in Taiwan are substantial. In particular, the Construction index is the major transmitter of shocks to other industries, and the Steel index, in contrast, suffers the most shocks from others. The spillover index fluctuates over time and indeed detects the severity of subprime mortgage crisis. The third essay adopts the multigroup factor analysis proposed by Goyal, Perignon and Villa (2008) to estimate the number of common pervasive factors for annual age-specific mortality for the entire U.S. populations. While the standard principal component analysis easily treats any group-specific factor as pervasive one due to its high contribution to total system variance, this methodology is able to estimate the space spanned by common and group-specific pervasive factors and recognize the true common factors. Empirical result shows that there are only two common pervasive factors governing the death rates in the United States; in particular, the importance of the second factor increases over time.

This research aims to improve the design and placement of runway exits at airports through analysis and modeling of the effects that exogenous causal factors have on pilots' landing behavior and exit selections. Incorporating these factors into modeling software will strengthen the software's utility by providing project teams the ability to specify which pilot motivational causal factors apply to a new or existing runway. The main findings suggest pilots' exit selections are deterministic but dependent on the presence (or absence) of six (6) causal factors. A model and two (2) case studies are presented and compared against predictions generated by existing modeling software. The results support a finding that the causal factor model improves motivation-based predictions over current modeling techniques, which are drawn from stochastic distributions. The accuracy of this model enables designers to optimize runway exit placement and geometry to maximize runway capacity. / Master of Science / Airport design engineers currently plan the locations and geometric characteristics of runway exits by balancing the expected fleet mix of aircraft on that runway with the capacity and delay effects that the number and placement of these exits might cause. This technique originated from research beginning in the early 1970s, which found that pilots' exit motivations primarily resulted from the capabilities and limitations of their aircraft. Since pilots tend to "fly by the numbers" (i.e., exhibit predictable approach airspeeds, power levels, wing flaps, touchdown locations, landing speeds, and braking efforts), engineers thus employed design principles in which the numbers, locations and geometries of exits were primarily functions of the physical and performance-based characteristics of the specific types of aircraft expected to utilize the runway. However, in studying more than 4 million landings by a single aircraft type (the Boeing 737-800) at 42 U.S. airports, the evidence in this thesis shows that pilots' exit selections are behaviorally motivated by more than the physics of motion. This thesis aims to refine previous research and engineering methods by showing evidence that pilots' exit selections have as much to do with the presence (or absence) of certain environmental factors within the landing system. These factors (described in detailed within) are unique to each airport's overall physical network of interconnected runways, exits, taxiways, terminals and other features. Within this network, a pilot's landing behavior and exit selection depends on the locational and relational interactions that each exit choice will have on the time and distance to their apron (gate) assignment. These "interactions" are referred to as causal factors – defined as physical features within a landing environment that pilots have little-to-no control over – but which nevertheless influence their specific exit selections. Two (2) runway case studies provided in this thesis evidence a finding that a causal factor model reliably predicts pilots' exit selections better than current modeling techniques, which are drawn from probability-based statistical distributions. The stability and accuracy of the new model enables engineering design and project teams to optimize runway exit placement and geometry to maximize runway capacity, and can be adopted for use in both existing and future runways.

臺灣的男女死亡率皆呈現逐年遞減的趨勢，自1993年進入高齡化社會後，預計將會在2018年進入高齡社會；人口不斷老化的結果讓社會上不論人民或是如保險公司等年金提供者皆面臨愈來愈嚴重的長壽風險；目前現有文獻提出了許多方式以解決長壽風險，其中多數的方法皆需使用到對未來死亡率之預估。 本研究為了能夠更準確的預估未來死亡率的趨勢，參考了Lee Carter (1992)所提出之模型以及Li and Lee (2005)、Li (2013)提出之共同改善趨勢效果，提出考慮商品與商品間以及商品與整體人口間共同改善趨勢之死亡率模型；本研究利用臺灣之保險公司壽險及年金業務經驗死亡率和Human Mortality Database之臺灣人口資料對模型進行配適，並以MAE、MAPE、RMSE三項指標比較與Lee Carter模型之優劣。 最後，本研究利用所配適之模型進行預測，模擬自然避險之效果，檢視臺灣保險業進行自然避險的可能效益，並對決策者在於決定是否要進行自然避險方面給出建議。 / Taiwan became an aging society in 1993 and is expected to become an aged society in 2018. The progressive decrease in Taiwan mortality since the 20th century for both genders has made longevity risk a serious problem for both people and annuity provider in Taiwan. So far, the literature has discussed about how to deal with longevity risk and came out with several solutions which can be categorize as “industry self-insurance”, “ mortality projection improvement” and “capital market solutions” , most of them are related to the projection of mortality. In order to provide a more precise projection of future mortality trend, this article designs several models which collaborates Lee Carter Model (1992) and the common improvement trend suggested by Li and Lee (2005). Based on our models, the Taiwan insurance industry experience mortality data and the Taiwan population mortality data, we test the performance of our models and make comparison. Lastly, we use the model we find to project future mortality trend and try to make a simulation of natural hedging strategy in Taiwan. The purpose we do this is to test the performance of natural hedging method and give suggestion for the decision-maker when they are considering whether to execute a natural hedging strategy.

La thèse étudie la dynamique et la persistance de l’inflation dans les pays en développement, particulièrement ceux des pays de la Zone UEMOA, en mettant en exergue les spécificités de ces économies. Le premier chapitre, consacré à l’évaluation de la persistance, révèle que le degré de persistance de l'inflation est faible dans ces pays, ce qui constitue un atout pour les autorités monétaires. Dans le chapitre 2, il a été défini un cadre théorique plus approprié à l’analyse de la persistance de l’inflation dans les pays de la sous-région. L’approche a permis de montrer que le degré de persistance de l’inflation dans ces pays ne dépendait pas uniquement des politiques monétaire et de change, mais aussi négativement du poids du secteur vivrier local dans l’économie. Dans le chapitre 3, la thèse analyse les écarts d’inflation dans les pays membres de l’UEMOA, en examinant la β-convergence des différentiels d'inflation. Les estimations révèlent que, d’une part, les écarts d’inflation se sont fortement réduits à l’intérieur de l'Union et que, d’autre part, ils restent fortement persistants avec la zone Euro. Le chapitre 4 est consacré à l’évaluation du rôle des différents facteurs et utilise ensuite une spécification spatiale en panel, pour tester les effets de contagion entre pays. Les estimations indiquent une prédominance des facteurs globaux et des effets de contagion entre pays dont l'ampleur dépend du poids des exportations de chaque pays vers les autres pays de la sous région. / This thesis examines the inflation dynamics and persistence in developing countries, especially in the UEMOA zone, highlighting the specificities of these economies. The first chapter, reveals that the inflation persistence degree, in these countries, is low which represents an asset to the monetary authorities. In Chapter 2, it was defined a more appropriate theoretical framework to analyze the inflation persistence in the countries of the sub-region. The approach allowed to demonstrate that the inflation persistence degree in these countries is not only dependent on monetary and exchange rate policies, but also negatively to the weight of local food sector in the economy. Chapter 3, analyzes the inflation differentials in the UEMOA member countries, by examining the β - convergence of inflation differentials. Estimations show that the inflation differentials are greatly reduced within the Union and they are highly persistent with the Euro zone. Chapter 4, is devoted to assessing the role of various factors and then uses a spatial panel specification to test the spillover effect between countries. Estimations indicate a predominance of global factors and contagion between countries whose magnitude depends on the weight of exports to other countries in the sub-region.

Cette thèse s’attache à développer des outils et modèles adaptés a l’étude de certains risques spatiaux et en réseaux. Elle est divisée en cinq chapitres. Le premier consiste en une introduction générale, contenant l’état de l’art au sein duquel s’inscrivent les différents travaux, ainsi que les principaux résultats obtenus. Le Chapitre 2 propose un nouveau générateur de précipitations multi-site. Il est important de disposer de modèles capables de produire des séries de précipitations statistiquement réalistes. Alors que les modèles précédemment introduits dans la littérature concernent essentiellement les précipitations journalières, nous développons un modèle horaire. Il n’implique qu’une seule équation et introduit ainsi une dépendance entre occurrence et intensité, processus souvent considérés comme indépendants dans la littérature. Il comporte un facteur commun prenant en compte les conditions atmosphériques grande échelle et un terme de contagion auto-regressif multivarié, représentant la propagation locale des pluies. Malgré sa relative simplicité, ce modèle reproduit très bien les intensités, les durées de sècheresse ainsi que la dépendance spatiale dans le cas de la Bretagne Nord. Dans le Chapitre 3, nous proposons une méthode d’estimation des processus maxstables, basée sur des techniques de vraisemblance simulée. Les processus max-stables sont très adaptés à la modélisation statistique des extrêmes spatiaux mais leur estimation s’avère délicate. En effet, la densité multivariée n’a pas de forme explicite et les méthodes d’estimation standards liées à la vraisemblance ne peuvent donc pas être appliquées. Sous des hypothèses adéquates, notre estimateur est efficace quand le nombre d’observations temporelles et le nombre de simulations tendent vers l’infini. Cette approche par simulation peut être utilisée pour de nombreuses classes de processus max-stables et peut fournir de meilleurs résultats que les méthodes actuelles utilisant la vraisemblance composite, notamment dans le cas où seules quelques observations temporelles sont disponibles et où la dépendance spatiale est importante / This thesis aims at developing tools and models that are relevant for the study of some spatial risks and risks in networks. The thesis is divided into five chapters. The first one is a general introduction containing the state of the art related to each study as well as the main results. Chapter 2 develops a new multi-site precipitation generator. It is crucial to dispose of models able to produce statistically realistic precipitation series. Whereas previously introduced models in the literature deal with daily precipitation, we develop a hourly model. The latter involves only one equation and thus introduces dependence between occurrence and intensity; the aforementioned literature assumes that these processes are independent. Our model contains a common factor taking large scale atmospheric conditions into account and a multivariate autoregressive contagion term accounting for local propagation of rainfall. Despite its relative simplicity, this model shows an impressive ability to reproduce real intensities, lengths of dry periods as well as the spatial dependence structure. In Chapter 3, we propose an estimation method for max-stable processes, based on simulated likelihood techniques. Max-stable processes are ideally suited for the statistical modeling of spatial extremes but their inference is difficult. Indeed the multivariate density function is not available and thus standard likelihood-based estimation methods cannot be applied. Under appropriate assumptions, our estimator is efficient as both the temporal dimension and the number of simulation draws tend towards infinity. This approach by simulation can be used for many classes of max-stable processes and can provide better results than composite-based methods, especially in the case where only a few temporal observations are available and the spatial dependence is high

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對於商業保險公司和政府單位而言，死亡率的改善和未來死亡率的預估一直是一大重要議題。特別是對於退休金相關的社會保險、勞退或是商業年金、壽險等等，如何找尋一個準確的預估模式對未來的死亡率改善情況進行預測，並釐訂合理的保費及提列適當的準備金，是對於一個保險制度能否永續經營的重要因素。過去所使用的配適方法，大多僅以單一群體的過去資料輔助未來的預測，例如 Li and Carter (1992)所提出的 Lee-Carter Model，或是 Bell (1997)使用主成分分析法 (Principal Component Analysis, PCA)等僅針對單一群體本身變數進行分析之方式。然而綜觀全球死亡率改善趨勢，可發現國與國間、組與祖間雖有不同，但仍具備共同的趨勢。因此在考慮未來的死亡率配適方面，應加入組與組間的共同因子 (common factors) 進行考量。 Li and Lee (2005)曾提出 Augmented Lee-Carter Model，即對原本的Lee-Carter Model進行修正，加入共同因素項，並且得到更好的預測效果。 本文則採用考慮共同因子之主成分分析原理建構多重群體死亡率模型，即透過主成分分析法，同時考慮不同群體間的死亡率，並以台灣男性和女性1970年至2010年的死亡率資料，做為兩個子群體進行分析。本文使用之主成分分析法模式，和 Lee-Carter Model (Li and Carter, 1992) 和 Augmented Lee-Carter Model (Li and Lee, 2005)，以MAPE法對個別的預測能力進行分析，並得出採用PCA的模式，在預測男性短年期(5年)內的預估能力屬精確(MAPE 介於10%~20%之間)，然而在長期預估下容易失準，且所有使用的模型，在配適台灣資料時皆發生無法準確預估嬰幼兒期(0~3歲)和老年期(80歲以上)之情形。本文並以所有模型預估之死亡率計算保險公司之準備金與保費提列，並與第五回經驗生命表進行比較。 / For governments and life insurance companies, mortality rates are one of the key factors in determining premiums and reserves. Ignoring or miscalculating mortality rates might have negative influences in pricing. However, most of the mortality models do not consider the common trends between groups. In this article, we try to construct the mortality structure which considering common trends of multi-groups populations with principal component analysis (PCA) method. We choose 9 factors to set up our model and fit with the actual data in Taiwan’s gender mortality. We also compare the Lee-Carter Model (Lee and Carter, 1992) and the augmented Lee-Carter Model (Li and Hardy, 2012) with our common factors PCA model, and we find that the PCA model has the least MAPE than other model in five years forecasting in both genders. After finishing basic analysis, we use the mortality data of Taiwan (1970 to 2010) from human mortality database to construct the life expectancy model. We adopt the same criteria to choose the components we need. We also compare the level premium and reserves by different forecasting mortality rates. All of the models indicate life insurance companies to provide higher reserves and level premium than using the 5th TSO experience mortality rare. We will do following research by using company-specific data to construct unique life expectancy model.