Cette thèse traite de la théorie du risque en finance et en assurance. La mise en pratique du concept de comonotonie, la dépendance du risque au sens fort, est décrite pour identifier l’optimum de Pareto et les allocations individuellement rationnelles Pareto optimales, la tarification des options et la quantification des risques. De plus, il est démontré que l’aversion au risque monotone à gauche, un raffinement pertinent de l’aversion forte au risque, caractérise tout décideur à la Yaari, pour qui, l’assurance avec franchise est optimale. Le concept de comonotonie est introduit et discuté dans le chapitre 1. Dans le cas de risques multiples, on adopte l’idée qu’une forme naturelle pour les compagnies d’assurance de partager les risques est la Pareto optimalité risque par risque. De plus, l’optimum de Pareto et les allocations individuelles Pareto optimales sont caractérisées. Le chapitre 2 étudie l’application du concept de comonotonie dans la tarification des options et la quantification des risques. Une nouvelle variable de contrôle de la méthode de Monte Carlo est introduite et appliquée aux “basket options”, aux options asiatiques et à la TVaR. Finalement dans le chapitre 3, l’aversion au risque au sens fort est raffinée par l’introduction de l’aversion au risque monotone à gauche qui caractérise l’optimalité de l’assurance avec franchise dans le modèle de Yaari. De plus, il est montré que le calcul de la franchise s’effectue aisément. / This thesis deals with the risk theory in Finance and Insurance. Application of the Comonotonicity concept, the strongest risk dependence, is described for identifying the Pareto optima and Individually Rational Pareto optima allocations, option pricing and quantification of risk. Furthermore it is shown that the left monotone risk aversion, a meaningful refinement of strong risk aversion, characterizes Yaari’s decision makers for whom deductible insurance is optimal. The concept of Comonotonicity is introduced and discussed in Chapter 1. In case of multiple risks, the idea that a natural way for insurance companies to optimally share risks is risk by risk Pareto-optimality is adopted. Moreover, the Pareto optimal and individually Pareto optimal allocations are characterized. The Chapter 2 investigates the application of the Comonotonicity concept in option pricing and quantification of risk. A novel control variate Monte Carlo method is introduced and its application is explained for basket options, Asian options and TVaR. Finally in Chapter 3 the strong risk aversion is refined by introducing the left-monotone risk aversion which characterizes the optimality of deductible insurance within the Yaari’s model. More importantly, it is shown that the computation of the deductible is tractable.

Ce travail de thèse porte sur les outils statistiques pour l'évaluation des maxima de charges de sloshing dans les cuves de méthaniers. Selon les caractéristiques du navire, son chargement et les conditions de navigation, un ballotement hydrodynamique est observé à l'intérieur des cuves, phénomène communément appelé sloshing. La détermination des charges qui s'appliquent à la structure est basée sur des mesures de pression d'impact au moyen d'essais sur maquette. Les maxima de pression par impact, extraits des mesures, sont étudiés. La durée d'un essai est équivalente à 5 heures au réel et insuffisante pour déterminer des maxima de pression associés à de grandes périodes de retour (40 ans). Un modèle probabiliste est nécessaire pour extrapoler les maxima de pression. Le modèle usuel est une loi de Weibull. Comme ce sont les valeurs extrêmes des échantillons qui nous intéressent, les ajustements sont aussi effectués par les lois des valeurs extrêmes et de Pareto généralisées via les méthodes de maximum par bloc et d'excès au-dessus d'un seuil.L'originalité du travail repose sur l'emploi d'un système alternatif, plus pertinent pour la capture des maxima de pression et d'une quantité de 480 heures de mesures disponible pour les mêmes conditions d'essai. Cela fournit une distribution de référence pour les maxima de pression et nous permet d'évaluer la pertinence des modèles sélectionnés. Nous insistons sur l'importance d'évaluer la qualité des ajustements par des tests statistiques et de quantifier les incertitudes sur les estimations obtenues. La méthodologie fournie a été implémentée dans un logiciel nommé Stat_R qui facilite la manipulation et le traitement des résultats. / This thesis focuses on statistical tools for the assessment of maxima sloshing loads in LNG tanks. According to ship features, tank cargo and sailing conditions, a sloshing phenomenon is observed inside LNG tanks. The determination of sloshing loads supported by the tank structure is derived from impact pressure measurements performed on a test rig. Pressure maxima per impact, extracted from test measurements, are investigated. Test duration is equivalent to 5 hours in full scale. This duration is not sufficient to determine pressure maxima associated with high return periods (40 years). It is necessary to use a probabilistic model in order to extrapolate pressure maxima. Usually, a Weibull model is used. As we focus on extreme values from samples, fittings are also performed with the generalized extreme value distribution and the generalized Pareto distribution using block maximum method and peaks over threshold method.The originality of this work is based on the use of an alternate measurement system which is more relevant than usual measurement system to get pressure maxima and a 480 hours measured data available for same test conditions. This provides a reference distribution for pressure maxima which is used to assess the relevance of the selected probabilistic models. Particular attention is paid to the assessment of fittings quality using statistical tests and to the quantification of uncertainties on estimated values.The provided methodology has been implemented in a software called Stat_R which makes the manipulation and the treatment of results easier.

To meet the exponentially increasing traffic data driven by the rapidly growing mobile subscriptions, both industry and academia are exploring the potential of a new genera- tion (5G) of wireless technologies. An important 5G goal is to achieve high data rate. Small cells with spectrum sharing and multiple-input multiple-output (MIMO) techniques are one of the most promising 5G technologies, since it enables to increase the aggregate data rate by improving the spectral efficiency, nodes density and transmission bandwidth, respectively. However, the increased interference in the densified networks will in return limit the achievable rate performance if not properly managed. The considered setup can be modeled as MIMO interference networks, which can be classified into the K-user MIMO interference channel (IC) and the K-cell MIMO interfering broadcast channel/multiple access channel (MIMO-IBC/IMAC) according to the number of mobile stations (MSs) simultaneously served by each base station (BS). The thesis considers two physical layer (PHY) resource allocation problems that deal with the interference for both models: 1) Pareto boundary computation for the achiev- able rate region in a K-user single-stream MIMO IC and 2) grouping-based interference alignment (GIA) with optimized IA-Cell assignment in a MIMO-IMAC under limited feedback. In each problem, the thesis seeks to provide a deeper understanding of the system and novel mathematical results, along with supporting numerical examples. Some of the main contributions can be summarized as follows. It is an open problem to compute the Pareto boundary of the achievable rate region for a K-user single-stream MIMO IC. The K-user single-stream MIMO IC models multiple transmitter-receiver pairs which operate over the same spectrum simultaneously. Each transmitter and each receiver is equipped with multiple antennas, and a single desired data stream is communicated in each transmitter-receiver link. The individual achievable rates of the K users form a K-dimensional achievable rate region. To find efficient operating points in the achievable rate region, the Pareto boundary computation problem, which can be formulated as a multi-objective optimization problem, needs to be solved. The thesis transforms the multi-objective optimization problem to two single-objective optimization problems–single constraint rate maximization problem and alternating rate profile optimization problem, based on the formulations of the ε-constraint optimization and the weighted Chebyshev optimization, respectively. The thesis proposes two alternating optimization algorithms to solve both single-objective optimization problems. The convergence of both algorithms is guaranteed. Also, a heuristic initialization scheme is provided for each algorithm to achieve a high-quality solution. By varying the weights in each single-objective optimization problem, numerical results show that both algorithms provide an inner bound very close to the Pareto boundary. Furthermore, the thesis also computes some key points exactly on the Pareto boundary in closed-form. A framework for interference alignment (IA) under limited feedback is proposed for a MIMO-IMAC. The MIMO-IMAC well matches the uplink scenario in cellular system, where multiple cells share their spectrum and operate simultaneously. In each cell, a BS receives the desired signals from multiple MSs within its own cell and each BS and each MS is equipped with multi-antenna. By allowing the inter-cell coordination, the thesis develops a distributed IA framework under limited feedback from three aspects: the GIA, the IA-Cell assignment and dynamic feedback bit allocation (DBA), respec- tively. Firstly, the thesis provides a complete study along with some new improvements of the GIA, which enables to compute the exact IA precoders in closed-form, based on local channel state information at the receiver (CSIR). Secondly, the concept of IA-Cell assignment is introduced and its effect on the achievable rate and degrees of freedom (DoF) performance is analyzed. Two distributed matching approaches and one centralized assignment approach are proposed to find a good IA-Cell assignment in three scenrios with different backhaul overhead. Thirdly, under limited feedback, the thesis derives an upper bound of the residual interference to noise ratio (RINR), formulates and solves a corresponding DBA problem. Finally, numerical results show that the proposed GIA with optimized IA-Cell assignment and the DBA greatly outperforms the traditional GIA algorithm.

Tato diplomová práce je zaměřena na vývoj simulačního prostředí v Matlab/Simulink zvoleného letadla ve známém letovém režimu. Pozice a orientace letadla pohybujícího se ve vzduchu je popsána pohybovými rovnicemi se šesti stup\v{n}i volnosti. Soustava translačních, rotačních a kinematických rovnic tvoří soustavu devíti nelineárních diferenciálních rovnic prvního řádu. Tyto rovnice lze linearizovat okolo nějakého rovnovážného stavu, který budeme nazývat letovým režimem. Součástí simulačního prostředí je řídící systém letadla založený na PID regulaci. Základem je návrh autopilota, který řídí úhel podélného sklonu a úhel příčného náklonu. Součástí návrhu jsou takzvané „flight director\textquotedblright \phantom{s}m\'dy jako udržení výšky, volba kursu, regulace vertikální rychlosti, změna výšky, zachycení požadované výšky a navigační m\'{o}d založený na nelineárním navigačním zákonu. Optimalizace regulátorů za použití PSO algoritmu a Pareto optimalitě je využita pro nastavení parametrů PID regulátoru. Simulační prostředí je vizualizováno v softwaru FlightGear.

This work concentrates on the study of mathematical models of human behaviour in dynamic games; in particular games with aspects of cooperation, implementation of a model and experimentation with the model. The game DarkElf was chosen for this project. It is a strategic, turn based game with economic and military features, where the decisions made by players are simultaneously implemented at a predetermined time.

To meet the exponentially increasing traffic data driven by the rapidly growing mobile subscriptions, both industry and academia are exploring the potential of a new genera- tion (5G) of wireless technologies. An important 5G goal is to achieve high data rate. Small cells with spectrum sharing and multiple-input multiple-output (MIMO) techniques are one of the most promising 5G technologies, since it enables to increase the aggregate data rate by improving the spectral efficiency, nodes density and transmission bandwidth, respectively. However, the increased interference in the densified networks will in return limit the achievable rate performance if not properly managed. The considered setup can be modeled as MIMO interference networks, which can be classified into the K-user MIMO interference channel (IC) and the K-cell MIMO interfering broadcast channel/multiple access channel (MIMO-IBC/IMAC) according to the number of mobile stations (MSs) simultaneously served by each base station (BS). The thesis considers two physical layer (PHY) resource allocation problems that deal with the interference for both models: 1) Pareto boundary computation for the achiev- able rate region in a K-user single-stream MIMO IC and 2) grouping-based interference alignment (GIA) with optimized IA-Cell assignment in a MIMO-IMAC under limited feedback. In each problem, the thesis seeks to provide a deeper understanding of the system and novel mathematical results, along with supporting numerical examples. Some of the main contributions can be summarized as follows. It is an open problem to compute the Pareto boundary of the achievable rate region for a K-user single-stream MIMO IC. The K-user single-stream MIMO IC models multiple transmitter-receiver pairs which operate over the same spectrum simultaneously. Each transmitter and each receiver is equipped with multiple antennas, and a single desired data stream is communicated in each transmitter-receiver link. The individual achievable rates of the K users form a K-dimensional achievable rate region. To find efficient operating points in the achievable rate region, the Pareto boundary computation problem, which can be formulated as a multi-objective optimization problem, needs to be solved. The thesis transforms the multi-objective optimization problem to two single-objective optimization problems–single constraint rate maximization problem and alternating rate profile optimization problem, based on the formulations of the ε-constraint optimization and the weighted Chebyshev optimization, respectively. The thesis proposes two alternating optimization algorithms to solve both single-objective optimization problems. The convergence of both algorithms is guaranteed. Also, a heuristic initialization scheme is provided for each algorithm to achieve a high-quality solution. By varying the weights in each single-objective optimization problem, numerical results show that both algorithms provide an inner bound very close to the Pareto boundary. Furthermore, the thesis also computes some key points exactly on the Pareto boundary in closed-form. A framework for interference alignment (IA) under limited feedback is proposed for a MIMO-IMAC. The MIMO-IMAC well matches the uplink scenario in cellular system, where multiple cells share their spectrum and operate simultaneously. In each cell, a BS receives the desired signals from multiple MSs within its own cell and each BS and each MS is equipped with multi-antenna. By allowing the inter-cell coordination, the thesis develops a distributed IA framework under limited feedback from three aspects: the GIA, the IA-Cell assignment and dynamic feedback bit allocation (DBA), respec- tively. Firstly, the thesis provides a complete study along with some new improvements of the GIA, which enables to compute the exact IA precoders in closed-form, based on local channel state information at the receiver (CSIR). Secondly, the concept of IA-Cell assignment is introduced and its effect on the achievable rate and degrees of freedom (DoF) performance is analyzed. Two distributed matching approaches and one centralized assignment approach are proposed to find a good IA-Cell assignment in three scenrios with different backhaul overhead. Thirdly, under limited feedback, the thesis derives an upper bound of the residual interference to noise ratio (RINR), formulates and solves a corresponding DBA problem. Finally, numerical results show that the proposed GIA with optimized IA-Cell assignment and the DBA greatly outperforms the traditional GIA algorithm.

The smartphone industry has grown immensely in recent years. The two leading platforms, Google Android and Apple iOS, each feature marketplaces offering hundreds of thousands of software applications, or apps. The vast selection has facilitated a maturing industry, with new business and revenue models emerging. As an app developer, basic statistics and data for one's apps are available via the marketplace, but also via third-party data sources. This report regards how mobile software is evaluated and rated quantitatively by both endusers and developers, and which metrics are relevant in this context. A selection of freely available third-party data sources and app monitoring tools is discussed, followed by introduction of several relevant statistical methods and data mining techniques. The main object of this thesis project is to investigate whether findings from app statistics can provide understanding in how to design more successful apps, that attract more downloads and/or more revenue. After the theoretical background, a practical implementation is discussed, in the form of an in-house application statistics web platform. This was developed together with the app developer company The Mobile Life, who also provided access to app data for 16 of their published iOS and Android apps. The implementation utilizes automated download and import from online data sources, and provides a web based graphical user interface to display this data using tables and charts. Using mathematical software, a number of statistical methods have been applied to the collected dataset. Analysis findings include different categories (clusters) of apps, the existence of correlations between metrics such as an app’s market ranking and the number of downloads, a long-tailed distribution of keywords used in app reviews, regression analysis models for the distribution of downloads, and an experimental application of Pareto’s 80-20 rule which was found relevant to the gathered dataset. Recommendations to the app company include embedding session tracking libraries such as Google Analytics into future apps. This would allow collection of in-depth metrics such as session length and user retention, which would enable more interesting pattern discovery. / Smartphonebranschen har växt kraftigt de senaste åren. De två ledande operativsystemen, Google Android och Apple iOS, har vardera distributionskanaler som erbjuder hundratusentals mjukvaruapplikationer, eller appar. Det breda utbudet har bidragit till en mognande bransch, med nya växande affärs- och intäktsmodeller. Som apputvecklare finns grundläggande statistik och data för ens egna appar att tillgå via distributionskanalerna, men även via datakällor från tredje part. Den här rapporten behandlar hur mobil mjukvara utvärderas och bedöms kvantitativt av båda slutanvändare och utvecklare, samt vilka data och mått som är relevanta i sammanhanget.  Ett urval av fritt tillgängliga tredjeparts datakällor och bevakningsverktyg presenteras, följt av en översikt av flertalet relevanta statistiska metoder och data mining-tekniker. Huvudsyftet med detta examensarbete är att utreda om fynd utifrån appstatistik kan ge förståelse för hur man utvecklar och utformar mer framgångsrika appar, som uppnår fler nedladdningar och/eller större intäkter. Efter den teoretiska bakgrunden diskuteras en konkret implementation, i form av en intern webplattform för appstatistik. Denna plattform utvecklades i samarbete med apputvecklaren The Mobile Life, som också bistod med tillgång till appdata för 16 av deras publicerade iOSoch Android-appar. Implementationen nyttjar automatiserad nedladdning och import av data från datakällor online, samt utgör ett grafiskt gränssnitt för att åskådliggöra datan med bland annat tabeller och grafer. Med hjälp av matematisk mjukvara har ett antal statistiska metoder tillämpats på det insamlade dataurvalet. Analysens omfattning inkluderar en kategorisering (klustring) av appar, existensen av en korrelation mellan mätvärden såsom appars ranking och dess antal nedladdningar, analys av vanligt förekommande ord ur apprecensioner, en regressionsanalysmodell för distributionen av nedladdningar samt en experimentell applicering av Paretos ”80-20”-regel som fanns lämplig för vår data. Rekommendationer till appföretaget inkluderar att bädda in bibliotek för appsessionsspårning, såsom Google Analytics, i dess framtida appar. Detta skulle möjliggöra insamling av mer detaljerad data såsom att mäta sessionslängd och användarlojalitet, vilket skulle möjliggöra mer intressanta analyser.

Zukünftige Beschleunigerprojekte und Nutzerexperimente erfordern für ihren Betrieb einen hochbrillanten Elektronenstrahl mit hohem mittlerem Strom. Eine Elektronenquelle mit dem Potential die Anforderungen erfüllen, ist ein supraleitender Hochfrequenz (SHF) Photoinjektor im Dauerstrichbetrieb. Die Strahldynamik eines solchen Photoinjektor Systems bestimmt die maximal zu erreichende Strahlbrillanz und wird ihrerseits von den Design und Betriebsparametern des Photoinjektors beeinflusst. Ziel ist immer die entscheidenden Design- und Betriebsparameter der Elektronenquelle hinsichtlich einer maximalen Strahlbrillanz zu wählen. Diese Aufgabe verlangt ein detailliertes Verständnis der Strahldynamik-Prozesse. Ferner ist es notwendig, eine Optimierung des Photoinjektors als Ganzes, mit dem Ziel einer maximalen Strahlqualität bei hohem mittlerem Strom, vorzunehmen. Dieses ermöglicht auch, die physikalischen Grenzen eines gegebenen Designs zu ermitteln und im Betrieb vollständig auszunutzen. Diese Doktorarbeit befasst sich mit der Strahldynamik in einem SHF Photoinjektor, unter Berücksichtigung interner Raumladungseffekte. Die Erkenntnisse zur Strahldynamik werden für die Entwicklung eines Optimierungsprogramms verwendet, um die Leistung des Injektors hinsichtlich der Strahlbrillanz zu verbessern. Die entwickelte Methode basiert auf Pareto-Optimierung mehrerer Zielfunktionen, unter Verwendung eines generischen Algorithmus. Das zentrale Ergebnis dieser Arbeit umfasst ein universelles Optimierungsprogramm, das für Photoinjektoren unabhängig von ihrem Design und Anwendungsgebiet genutzt werden kann. Für den Betrieb mit hoher Strahlbrillanz ist es möglich aus den erhaltenen Pareto-optimalen Lösungen einen stabilen Satz an Einstellwerten für den Photoinjektor zu extrahieren. Durch die allgemeine Optimierungsstrategie lässt sich das entwickelte Programm auch für andere Beschleunigerabschnitte, oder die Optimierung einer ganzen Anlage mit erweiterter Zielsetzung anpassen. / An increasing number of future accelerator projects, light sources and user experiments require high brightness, high average current electron beams for operation. Superconducting radio-frequency (SRF) photoinjectors running in continuous-wave (cw) mode hold the potential to serve as an electron source that generates electron beams of high brightness. Different operation and design parameters of the SRF photoinjector impact the beam dynamics and, thus, the beam brightness. Therefore, an in-depth understanding of the beam dynamics processes in an SRF photoinjector and the dependency of the beam dynamics on the photoinjector set parameters is crucial. A high brightness beam operation requires a global optimization of the SRF photoinjector that allows to find suitable photoinjector settings and to figure out and extend the physical performance limits of the investigated injector design. The dissertation at hand offers a detailed analysis of the beam dynamics in an SRF photoinjector regarding internal space charge effects. Furthermore, the impact of the photoinjector elements on the electron beam is discussed. The lessons learned from this theoretical view are implemented in the development of an optimization tool to achieve a high brightness performance. A universal multi-objective optimization program based on a generic algorithm was developed to extract stable, optimum gun parameter from Pareto-optimum solutions. This universal tool is able to optimize and find the physical performance limit of any (S)RF photoinjector independent from the individual application of the electron source (energy recovery linac, free electron laser, ultra-fast electron diffraction). This thesis thereby verifies and complements existing theoretical considerations regarding photoinjector-beam interactions. The global optimization strategy can be introduced to variable optimization objectives as well as it can be extended to an optimization of further parts of the accelerator facility.

於理論上，自由市場透過「價格機能」之運作，將使資源之配置與使用達到最高效率 ，然此市場之運作需有某些前提–完全競爭及無外溢效果等方能成立。但於現實社會 中上述假設前提並不存在，致使柏拉圖的最適境界(pareto optimal)無法達成，尤其 是具有異質性，不可移動性、不可增減性之土地，更易導致土地市場的地理區隔及非 完全競爭等現象；外部性及公共財不足之市場失靈(Market Failure)問題更是伏拾皆 是；再者和經濟部門為追求最大利潤，往往罔顧社會成本，導致不當的土地配置與使 用。故政府之適當干預確有其必要，而土地規劃與管制則係反應此種需要，以修正及 彌補土地市場之缺失，俾達土地之合理配置與使用。 然而，土地規劃管制之實施過程中，由於各宗土地使用類別與密度之差異，或變更使 用等，往往對地價造成上漲或下只之經濟效果，導致土地所有權人間之利得(windfa- ll) 或損失(wipeout) 之不公平現象，實有待積極改善。處理此類公平性問題的方法 有許多，例如區段征收、市地重劃、發展權移轉(T.D.R) 及稅捐等方式，本研究乃選 擇我國土地政策之最高指導原則–平均地權之主要政策手段–土地稅–進行研究。此 外，如何運用土地稅來促進土地規劃與使用管制目標之達成，亦為本研究之範圍。 故本研究擬基於效率與公平之觀點，參考國外土地稅制針對我國土地稅之課稅時機、 課稅方式、稅基、稅率結構等予以檢討分析，俾能改進現行之地價稅、土地增值稅與 空地稅的課征，以達平均地權之地盡其利與地利共享之崇高目標。 全文計六章，分別為： 第一章 緒論 第二章 文獻回顧 第三章 土地規劃管制與其公平性之探討 第四章 土地稅促進土地規劃管制實施之分析 第五章 現行我國土地稅制之檢討與改進措施 第六章 結論與建議

The US sub-prime mortgage crisis greatly affected not only the US economy but also other countries in the world. This thesis employs the extreme value theory and Value at Risk (VaR) analysis to assess the impact of the US sub-prime mortgage crisis on various stock markets of the MSCI indexes, including 10 countries and 7 areas. It is reasonable to guess that VaR value should increase after the crisis. The empirical analyses on these indexes conclude that (1) the American market indexes not only do not agree with the guess after the crisis but four American indexes are identical; (2) not all the Asia market indexes consist with the guess; (3) the European market indexes agree with the guess; (4) MSCI AC PACIFIC, NEW ZEALAND, and AUSTRALIA consist with the guess; (5) the behavior for the positive log returns is different from that for the negative returns in some MSCI indexes. Over speaking, the impacts of US sub-prime mortgage crisis on those countries are not the same.