Global ETD Search

1	Quantitative analysis of extreme risks in insurance and finance Yuan, Zhongyi 01 May 2013 (has links) In this thesis, we aim at a quantitative understanding of extreme risks. We use heavy-tailed distribution functions to model extreme risks, and use various tools, such as copulas and MRV, to model dependence structures. We focus on modeling as well as quantitatively estimating certain measurements of extreme risks. We start with a credit risk management problem. More specifically, we consider a credit portfolio of multiple obligors subject to possible default. We propose a new structural model for the loss given default, which takes into account the severity of default. Then we study the tail behavior of the loss given default under the assumption that the losses of the obligors jointly follow an MRV structure. This structure provides an ideal framework for modeling both heavy tails and asymptotic dependence. Using HRV, we also accommodate the asymptotically independent case. Multivariate models involving Archimedean copulas, mixtures and linear transforms are revisited. We then derive asymptotic estimates for the Value at Risk and Conditional Tail Expectation of the loss given default and compare them with the traditional empirical estimates. Next, we consider an investor who invests in multiple lines of business and study a capital allocation problem. A randomly weighted sum structure is proposed, which can capture both the heavy-tailedness of losses and the dependence among them, while at the same time separates the magnitudes from dependence. To pursue as much generality as possible, we do not impose any requirement on the dependence structure of the random weights. We first study the tail behavior of the total loss and obtain asymptotic formulas under various sets of conditions. Then we derive asymptotic formulas for capital allocation and further refine them to be explicit for some cases. Finally, we conduct extreme risk analysis for an insurer who makes investments. We consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another autoregressive process, independent of the former one. We derive an asymptotic formula for the finite-time ruin probability and propose a hybrid method, combining simulation with asymptotics, to compute this ruin probability more efficiently. As an application, we consider a portfolio optimization problem in which we determine the proportion invested in the risky stock that maximizes the expected terminal wealth subject to a constraint on the ruin probability. Asymptotic dependence Asymptotics Capital allocation Copula Heavy-tailed distribution Multivariate regular variation Statistics and Probability
2	A Comparison Study on Natural and Head/tail Breaks Involving Digital Elevation Models Lin, Yue January 2013 (has links) The most widely used classification method for statistical mapping is Jenks’s natural breaks. However, it has been found that natural breaks is not good at classifying data which have scaling property. Scaling property is ubiquitous in many societal and natural phenomena. It can be explained as there are far more smaller things than larger ones. For example, there are far more shorter streets than longer ones, far more smaller street blocks than bigger ones, and far more smaller cities than larger ones. Head/tail breaks is a new classification scheme that is designed for values that exhibit scaling property. In Digital Elevation Models (DEMs), there are far more lower elevation points than higher elevation points. This study performs both head/tail breaks and natural breaks for values from five resolutions of DEMs. The aim of this study is to examine advantages and disadvantages of head/tail breaks classification scheme compared with natural breaks. One of the five resolutions of DEMs is given as an example to illustrate the principle behind the head/tail breaks in the case study.The results of head/tail breaks for five resolutions are slightly different from each other in number of classes or level of details. The similar results of comparisons support the previous finding that head/tail breaks is advantaged over natural breaks in reflecting the hierarchy of data. But the number of classes could be reduced for better statistical mapping. Otherwise the top values, which are very little, would be nearly invisible in the map.A main conclusion to be drawn from this study is that head/tail breaks classification scheme is advantaged over natural breaks in presenting hierarchy or scaling of elevation data, with the top classes gathered into one. Another conclusion is when the resolution gets higher; the scaling property gets more striking. Head/tail breaks natural breaks heavy-tailed distribution scaling property data classification digital elevation models
3	Statistické odhady a chvosty jejich rozdělení pravděpodobností / Statistické odhady a chvosty jejich rozdělení pravděpodobností Veverková, Jana January 2012 (has links) Master Thesis Statistical estimators and their tail behavior provides description of two type of characteristics of robustness of estimators - tail behavior and break- down point. Description is made for translation equivariant estimators in general and also for some concrete type of estimators, sample mean, sample median, trimmed mean, Huber estimator and Hodges Lehmann estimator. Tail behavior of these estimator is illustrated for random sample coming from t-distribution with 1 to 5 degrees of freedom. Ilustration is based on simulations made in Mathematica. 1
4	Velké odchylky a jejich aplikace v pojistné matematice / Large deviations and their applications in insurance mathematics Fuchsová, Lucia January 2011 (has links) Title: Large deviations and their applications in insurance mathematics Author: Lucia Fuchsová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Zbyněk Pawlas, Ph.D. Supervisor's e-mail address: Zbynek.Pawlas@mff.cuni.cz Abstract: In the present work we study large deviations theory. We discuss heavy-tailed distributions, which describe the probability of large claim oc- curence. We are interested in the use of large deviations theory in insurance. We simulate claim sizes and their arrival times for Cramér-Lundberg model and first we analyze the probability that ruin happens in dependence on the parameters of our model for Pareto distributed claim size, next we compare ruin probability for other claim size distributions. For real life data we model the probability of large claim size occurence by generalized Pareto distribu- tion. 1
5	The Principle of Scaling of Geographic Space and its Application in Urban Studies Liu, Xintao January 2012 (has links) Geographic space is the large-scale and continuous space that encircles the earth and in which human activities occur. The study of geographic space has drawn attention in many different fields and has been applied in a variety of studies, including those on cognition, urban planning and navigation systems. A scaling property indicates that small objects are far more numerous than large ones, i.e., the size of objects is extremely diverse. The concept of scaling resembles a fractal in geometric terms and a power law distribution from the perspective of statistical physics, but it is different from both in terms of application. Combining the concepts of geographic space and scaling, this thesis proposes the concept of the scaling of geographic space, which refers to the phenomenon that small geographic objects or representations are far more numerous than large ones. From the perspectives of statistics and mathematics, the scaling of geographic space can be characterized by the fact that the sizes of geographic objects follow heavy-tailed distributions, i.e., the special non-linear relationships between variables and their probability. In this thesis, the heavy-tailed distributions refer to the power law, lognormal, exponential, power law with an exponential cutoff and stretched exponential. The first three are the basic distributions, and the last two are their degenerate versions. If the measurements of the geographic objects follow a heavy-tailed distribution, then their mean value can divide them into two groups: large ones (a low percentage) whose values lie above the mean value and small ones (a high percentage) whose values lie below. This regularity is termed as the head/tail division rule. That is, a two-tier hierarchical structure can be obtained naturally. The scaling property of geographic space and the head/tail division rule are verified at city and country levels from the perspectives of axial lines and blocks, respectively. In the study of geographic space, the most important concept is geographic representation, which represents or partitions a large-scale geographic space into numerous small pieces, e.g., vector and raster data in conventional spatial analysis. In a different context, each geographic representation possesses different geographic implications and a rich partial knowledge of space. The emergence of geographic information science (GIScience) and volunteered geographic information (VGI) greatly enable the generation of new types of geographic representations. In addition to the old axial lines, this thesis generated several types of representations of geographic space: (a) blocks that were decomposed from road segments, each of which forms a minimum cycle such as city and field blocks (b) natural streets that were generated from street center lines using the Gestalt principle of good continuity; (c) new axial lines that were defined as the least number of individual straight line segments mutually intersected along natural streets; (d) the fewest-turn map direction (route) that possesses the hierarchical structure and indicates the scaling of geographic space; (e) spatio-temporal clusters of the stop points in the trajectories of large-scale floating car data. Based on the generated geographic representations, this thesis further applies the scaling property and the head/tail division rule to these representations for urban studies. First, all of the above geographic representations demonstrate the scaling property, which indicates the scaling of geographic space. Furthermore, the head/tail division rule performs well in obtaining the hierarchical structures of geographic objects. In a sense, the scaling property reveals the hierarchical structures of geographic objects. According to the above analysis and findings, several urban studies are performed as follows: (1) generate new axial lines based on natural streets for a better understanding of urban morphologies; (2) compute the fewest-turn and shortest map direction; (3) identify urban sprawl patches based on the statistics of blocks and natural cities; (4) categorize spatio-temporal clusters of long stop points into hotspots and traffic jams; and (5) perform an across-country comparison of hierarchical spatial structures. The overall contribution of this thesis is first to propose the principle of scaling of geographic space as well as the head/tail division rule, which provide a new and quantitative perspective to efficiently reduce the high degree of complexity and effectively solve the issues in urban studies. Several successful applications prove that the scaling of geographic space and the head/tail division rule are inspiring and can in fact be applied as a universal law, in particular, to urban studies and other fields. The data sets that were generated via an intensive geo-computation process are as large as hundreds of gigabytes and will be of great value to further data mining studies. / <p>QC 20120301</p> / Hägerstrand project entitled “GIS-based mobility information for sustainable urban planning and design” geographic space scaling GIScience VGI OSM heavy-tailed distribution the head/tail division rule space syntax nature street urban sprawl floating car data hierarchical spatial structure
6	Dépendance et événements extrêmes en théorie de la ruine : étude univariée et multivariée, problèmes d'allocation optimale / Dependence and extreme events in ruin theory : univariate and multivariate study, optimal allocation problems Biard, Romain 07 October 2010 (has links) Cette thèse présente de nouveaux modèles et de nouveaux résultats en théorie de la ruine, lorsque les distributions des montants de sinistres sont à queue épaisse. Les hypothèses classiques d’indépendance et de stationnarité, ainsi que l’analyse univariée sont parfois jugées trop restrictives pour décrire l’évolution complexe des réserves d’une compagnie d’assurance. Dans un contexte de dépendance entre les montants de sinistres, des équivalents de la probabilité deruine univariée en temps fini sont obtenus. Cette dépendance, ainsi que les autres paramètres du modèle sont modulés par un processus Markovien d’environnement pour prendre en compte des possibles crises de corrélation. Nous introduisons ensuite des modèles de dépendance entre les montants de sinistres et les temps inter-sinistres pour des risques de type tremblements de terre et inondations. Dans un cadre multivarié, nous présentons divers critères de risques tels que la probabilité de ruine multivariée ou l’espérance de l’intégrale temporelle de la partie négative du processus de risque. Nous résolvons des problèmes d’allocation optimale pour ces différentes mesures de risque. Nous étudions alors l’impact de la dangerosité des risques et de la dépendance entre les branches sur cette allocation optimale / This PhD thesis presents new models and new results in ruin theory, in the case where claim amounts are heavy-tailed distributed. Classical assumptions like independence and stationarity and univariate analysis are sometimes too restrictive to describe the complex evolution of the reserves of an insurance company. In a dependence context, asymptotics of univariate finite-time ruin probability are computed. This dependence, and the other model parameters are modulated by a Markovian environment process to take into account possible correlation crisis. Then, we introduce some models which describe dependence between claim amounts and claim interarrival times we can find in earthquake or flooding risks. In multivariate framework, we present some risk criteria like multivariate ruin probability or the expectation of the timeintegrated negative part of the risk process. We solve some problems of optimal allocation for these risk measures. Then, we study the impact of the risk dangerousness and of the dependence between lines on this optimal allocation. Théorie de la ruine Distribution à queue épaisse Dépendance spatio-temporelle Processus multivarié Allocation optimale Ruin theory Heavy-tailed distribution Spatio-temporal dependence Multivariate process Optimal allocation
7	Geospatial Knowledge Discovery using Volunteered Geographic Information : a Complex System Perspective Jia, Tao January 2012 (has links) The continuous progression of urbanization has resulted in an increasing number of people living in cities or towns. In parallel, advancements in technologies, such as the Internet, telecommunications, and transportation, have allowed for better connectivity among people. This has engendered drastic changes in urban systems during the recent decades. From a social geographic perspective, the changes in urban systems are primarily characterized by intensive contacts among people and their interactions with the surrounding urban environment, which further leads to subsequent challenging problems such as traffic jams, environmental pollution, urban sprawl, etc. These problems have been reported to be heterogeneous and non-deterministic. Hence, to cope with them, massive amounts of geographic data are required to create new knowledge on urban systems. Due to the thriving of Volunteer Geographic Information (VGI) in recent years, this thesis presents knowledge on urban systems based on extensive VGI datasets from three sources: highway dataset from the OpenStreetMap (OSM) project, photo location dataset from the Flickr website, and GPS tracking datasets from volunteers, taxicabs, and air flights. The knowledge primarily relates to two issues of urban systems: the urban space and the corresponding human dynamics. In accordance, on one hand, urban space acts as a carrier for associated geographic activities and knowledge of it benefits our understanding of current social and economic problems in urban systems. On the other hand, human dynamics reflect human behavior in urban space, which leads to complex mobility or activity patterns. Its investigation allows a derivation of the underlying driving force that is very instructive to urban planning, traffic management, and infectious disease control. Therefore, to fully understand the two issues, this thesis conducts a thorough investigation from multiple aspects. The first issue is investigated from four aspects. First, at the city level, the controversial topic of city size regularity is investigated in terms of natural cities, and the conclusion is that Zipf’s law holds stably for all US cities. Second, at the sub-city level, the size distribution of spatial units within different cities in terms of the clusters formed by street nodes, photo locations, and taxi static points are explored, and the result shows a remarkable scaling property of these spatial units. Third, enlightened by the scaling property of the urban space at the city or sub-city level, this thesis devises a novel tool that can demarcate the cities into three categories: compact cities, normal cities, and sprawling cities. The tool is then applied to cities in both the US and three European countries. In the last, another representation of urban space is taken into account, namely the transportation network. The findings report that the US airport network displays the properties of scale-free, small-world, and disassortative mixing and that the individual natural airports show heterogeneous patterns that are probably subject to geographic constraints and socioeconomic factors. The second issue is examined from four perspectives. First, at the city level, the movement flow contributed by agents using two types of behavior is investigated through an agent-based simulation, and the result conjectures that the human mobility behavior is mainly shaped by the underlying street network. Second, at the country level, this thesis reports that the human travel length by air can be approximated well by an exponential distribution, and subsequent simulations indicate that human mobility behavior is largely constrained by the underlying airport network. Third, at the regional level, the length that humans travel by car is demonstrated to agree well with a power law with exponential cutoff distribution, and subsequent simulation further reproduces this levy flight characteristic. Based on the simulation, human mobility behavior is again revealed to be primarily shaped by the underlying hierarchical spatial structure. Finally, taxicab static points are adopted to explore human activity patterns, which can be characterized as the regularities in space and time, the heterogeneity and predictability in space. From a complex system perspective, this thesis presents the knowledge discovered in urban systems using massive volumes of geographic data. Together with new knowledge from empirical findings, the development of methods, and the design of theoretic models, this thesis also shares the research community with geographic data generated from extensive VGI datasets and the corresponding source codes. Moreover, this study is aligned with a paradigm shift in that it analyzes large-size datasets using high processing power as opposed to analyzing small-size datasets with low processing power. / <p>QC 20121113</p> knowledge discovery urban systems complex system VGI OSM GPS tracking dataset scaling heavy-tailed distribution detection urban sprawl Zipf’s law human activity/mobility patterns agent-based modeling complex network.
8	Adaptive risk management Chen, Ying 13 February 2007 (has links) In den vergangenen Jahren ist die Untersuchung des Risikomanagements vom Baselkomitee angeregt, um die Kredit- und Bankwesen regelmäßig zu aufsichten. Für viele multivariate Risikomanagementmethoden gibt es jedoch Beschränkungen von: 1) verlässt sich die Kovarianzschätzung auf eine zeitunabhängige Form, 2) die Modelle beruhen auf eine unrealistischen Verteilungsannahme und 3) numerische Problem, die bei hochdimensionalen Daten auftreten. Es ist das primäre Ziel dieser Doktorarbeit, präzise und schnelle Methoden vorzuschlagen, die diesen Beschränkungen überwinden. Die Grundidee besteht darin, zuerst aus einer hochdimensionalen Zeitreihe die stochastisch unabhängigen Komponenten (IC) zu extrahieren und dann die Verteilungsparameter der resultierenden IC beruhend auf eindimensionale Heavy-Tailed Verteilungsannahme zu identifizieren. Genauer gesagt werden zwei lokale parametrische Methoden verwendet, um den Varianzprozess jeder IC zu schätzen, das lokale Moving Window Average (MVA) Methode und das lokale Exponential Smoothing (ES) Methode. Diese Schätzungen beruhen auf der realistischen Annahme, dass die IC Generalized Hyperbolic (GH) verteilt sind. Die Berechnung ist schneller und erreicht eine höhere Genauigkeit als viele bekannte Risikomanagementmethoden. / Over recent years, study on risk management has been prompted by the Basel committee for the requirement of regular banking supervisory. There are however limitations of many risk management methods: 1) covariance estimation relies on a time-invariant form, 2) models are based on unrealistic distributional assumption and 3) numerical problems appear when applied to high-dimensional portfolios. The primary aim of this dissertation is to propose adaptive methods that overcome these limitations and can accurately and fast measure risk exposures of multivariate portfolios. The basic idea is to first retrieve out of high-dimensional time series stochastically independent components (ICs) and then identify the distributional behavior of every resulting IC in univariate space. To be more specific, two local parametric approaches, local moving window average (MWA) method and local exponential smoothing (ES) method, are used to estimate the volatility process of every IC under the heavy-tailed distributional assumption, namely ICs are generalized hyperbolic (GH) distributed. By doing so, it speeds up the computation of risk measures and achieves much better accuracy than many popular risk management methods. Risikomanagement Heavy-Tailed Verteilung Lokale parametrische Methoden Hochdimensionale Datenanalyse Risk management Heavy-tailed distribution Local parametric methods High-dimensional data analysis 330 Wirtschaft 17 Wirtschaft QP 300 ddc:330
9	Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement El-Khatib, Mayar January 2010 (has links) While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond. highway development decision making under uncertainty real options jump processes infinitely divisible distributions Lévy processes measure theory characteristic function characteristic exponent Lévy jump measure probability measure cádlág stochastic process Wiener process Poisson process compound Poisson process finite activity models jump diffusion models Merton model Gaussian jump process Kou model double exponential jump process leptokurtic volatility smile infinite activity models pure jumps process generalized hyperbolic model modified Bessel function negative inverse Gaussian model geometric Brownian motion model log-normal distribution model normality assumption heavy-tailed distribution asymmetric distribution quantile-quantile plot Rydberg algorithm parameter calibration moments cummulants sum of squares Monte Carlo simulation least-squares regression backward dynamic programming discrete-time Markov chain land price traffic demand highway service quality index data collection traffic volume Annual Average Daily Traffic Ontario Ministry of Transportation Land Registry Office Freedom of Information Act seasonality value of transportation types of transportation systems importance of highway systems cost of wrong decisions monetary cost private sector cost human cost land expropriation environmental cost irreversibility cost factor time cost factor political cost factor opportunity cost opportunity cost of wrong decisions economic cost of wrong decisions economic cost of mis-estimation economic profit of wrong decisions cost of inaction price of making right decisions scope of decisions rehabilitation decision land acquisition decision expansion decision uncertainty modeling land acquisition cost expropriation cost construction cost material cost Montréal-Mirabel International Airport Pickering Airport 407 Express Toll Route Highway 407 Statistics
10	Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement El-Khatib, Mayar January 2010 (has links) While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond. highway development decision making under uncertainty real options jump processes infinitely divisible distributions Lévy processes measure theory characteristic function characteristic exponent Lévy jump measure probability measure cádlág stochastic process Wiener process Poisson process compound Poisson process finite activity models jump diffusion models Merton model Gaussian jump process Kou model double exponential jump process leptokurtic volatility smile infinite activity models pure jumps process generalized hyperbolic model modified Bessel function negative inverse Gaussian model geometric Brownian motion model log-normal distribution model normality assumption heavy-tailed distribution asymmetric distribution quantile-quantile plot Rydberg algorithm parameter calibration moments cummulants sum of squares Monte Carlo simulation least-squares regression backward dynamic programming discrete-time Markov chain land price traffic demand highway service quality index data collection traffic volume Annual Average Daily Traffic Ontario Ministry of Transportation Land Registry Office Freedom of Information Act seasonality value of transportation types of transportation systems importance of highway systems cost of wrong decisions monetary cost private sector cost human cost land expropriation environmental cost irreversibility cost factor time cost factor political cost factor opportunity cost opportunity cost of wrong decisions economic cost of wrong decisions economic cost of mis-estimation economic profit of wrong decisions cost of inaction price of making right decisions scope of decisions rehabilitation decision land acquisition decision expansion decision uncertainty modeling land acquisition cost expropriation cost construction cost material cost Montréal-Mirabel International Airport Pickering Airport 407 Express Toll Route Highway 407 Statistics

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