This project discusses the intensity and survival probability derived from Credit Default Swaps (CDS). We utilize two models, the reduced intensity model and the Shift Square Root Diffusion (SSRD) model. In the reduced intensity model, we assume a deterministic intensity and implement a computer simulation to derive the survival probability and intensity from the CDS market quotes of the company. In the SSRD model, the interest rate and intensity are both stochastic and correlated. We discuss the impaction of correlation on the interest rate and intensity. We also conduct a Monte Carlo simulation to determine the dynamics of stochastic interest rate and intensity.

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Background: Hepatocellular carcinoma (HCC) is the leading cause of cancer in Taiwan, which consumes high medical expense among the total healthcare expenditure and becomes the significant burden to the finance of National Health Insurance (NHI). However, population-based statistics about the cost with the survival rate is rare. Objective: Through analyzing the data from the Bureau of National Health Insurance and hospital clinical files, we estimated the medical expenditure for treating HCC patients and the factors associated with treatment outcome. Methods: The National Health Insurance data from 1996 to 2002 with ICD-9 code 155 were used, which include age, gender, visiting time, and medical cost for inpatient or outpatient visits. The population-based data were analyzed to estimate 1-5 year survival probability and medical cost of HCC patients. In hospital-based data, 189 patients from 1991 to 2004 were recorded by clinical chart and 62 of them diagnosed during 2002 and 2004 were further selected to match the claim data. These informations were used for computing survival or recurrence probability, related factors, and medical cost. Results: For all incident cases in 1997, the average 5-year cumulated cost was NT$ 219,398, while the cumulated cost for those patients survived more than five years was NT$ 491,288. The survival probability was 30.8% for more than one year, 20.9% for more than two years, 15.2% for more than three years, 11.3% for more than four years, and 9.7% for more than five years in 1997 respectively. Female and those age >45-65 years old seemed to have better survival outcomes than male and those age ¡Ø45 years old or >65 years old , the averaged medical cost per treated case surviving more than five years were T$2,457,214 for male and NT$ 1,987,874 for female. Hospital clinical data indicated that TNM stages, therapy choice, liver cirrhosis, and ascites are risk factors for surviving. Although pre-TACE treatment has higher expenditure, its five-year survival probability is better than other treatments in this research. Conclusions: This paper presents medical cost with survival probability and its associated factors for HCC patients and further estimates the medical cost per life saved for treating HCC patients. Our findings can offer the policy-maker, provider, and patient to evaluate the intervention or prevention program in the future.

The goal of this dissertation is to further our understanding of how spatially heterogeneous landscapes may impact the formation of range boundaries that then aggregate to form large-scale biodiversity patterns. These patterns have been analyzed from many different perspectives by ecologists, evolutionary biologist, and physiologists using a variety of different theoretical, statistical, and mechanistic models. For some species, there is an obvious abrupt change in the environment causing a range boundary. Other environments change gradually, and it is unclear why species fail to adapt and expand their range. The first chapter develops a novel theoretical model of how the establishment of new mutations allows for adaptation to an environmental gradient, when there is no genetic variation for the trait that limits the range. Shallow environmental gradients favor mutations that arise nearer to the range margin, have smaller phenotypic effects, and allow for proportionately larger expansions than steep gradients. Mutations that allow for range expansion tend to have large phenotypic effects causing substantial range expansions. Spatial and temporal variation in climatic and environmental variables is important for understanding species response to climate change. The second chapter uses a mechanistic model to simulate switchgrass (Panicum virgatum L.) productivity across the central and eastern U.S. for current and future climate conditions. Florida and the Gulf Coast of Texas and Louisiana have the highest predicted current and future yields. Regions where future temperature and precipitation are anticipated to increase, larger future yields are expected. Large-scale geographic patterns of biodiversity are documented for many taxa. The mechanisms allowing for the coexistence of more of species in certain regions are poorly understood. The third chapter employs a newly developed wavelet lifting technique to extract scale-dependent patterns from irregularly spaced two-dimensional ecological data and analyzes the relationship between breeding avian richness and four energy variables. Evapotranspiration, temperature, and precipitation are significant predictors of richness at intermediate-to-large scales. Net primary production is the only significant predictor across small-to-large scales, and explains the most variation in richness (~40%) at an intermediate scale. Changes in the species-energy relationship with scale, may indicate a shift in the mechanism governing species richness. / text

Title: Study of diffractive processes at the ATLAS Experiment Author: Vlastimil Kůs Department: Institute of Particle and Nuclear Physics Supervisor: Mgr. Marek Taševský, Ph.D. Institute of Physics of the Academy of Sciences of the CR, v.v.i. Abstract: A data sample of pp collisions corresponding to an integrated lumi- nosity of 6.75 nb−1 was collected at √ s = 7 TeV using the ATLAS detector at the Large Hadron Collider. Collision events with at least two jets with pT > 20 GeV are used to measure the differential cross section of the diffractive dijet production as a function of the rapidity gap size ∆ηF , the largest forward region extending from |η| = 4.8 devoid of particle activity above threshold momentum cuts, and an estimator of the fractional momentum loss of the scattered proton assuming the single diffractive dissociation (pp → pX), ˜ξ± . Comparisons with various Monte Carlo models reveal that though the region of small ˜ξ± and large rapidity gaps is dominated by diffraction, a contribution form non-diffractive events cannot be neglected. The rapidity gap survival probability is estimated based on data to Monte Carlo comparisons in the −3.2 < log10 ˜ξ± < −2.5 region of the ˜ξ± distri- bution with the ∆ηF > 2 requirement. 1

Complex processes whose evolution in time rests on the occurrence of a large and random number of intermittent events are the systems under study. The mean time distance between two consecutive events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that explains why the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories, each of which fits the stochastic central limit theorem and the condition for the Mittag-Leffler universality. Additionally, the effect of noise on the generation of the Mittag-Leffler function is discussed. Fluctuations of relatively weak intensity can conceal the asymptotic inverse power law behavior of the Mittag-Leffler function, providing a reason why stretched exponentials are frequently found in nature. These results afford a more unified picture of complexity resting on the Mittag-Leffler function and encompassing the standard inverse power law definition.

La théorie des processus de branchement multi-type en environnement i.i.d. est considérablement moins développée que dans le cas univarié, et les questions fondamentales ne sont pas résolues en totalité à ce jour. Les réponses exigent une compréhension profonde du comportement des produits des matrices i.i.d. à coefficients positifs. Sous des hypothèses assez générales et lorsque les fonctions génératrices de probabilité des lois de reproduction sont “linéaire fractionnaires”, nous montrons que la probabilité de survie à l’instant n du processus de branchement multi-type en environnement aléatoire est proportionnelle à 1/√n lorsque n → ∞. La démonstration de ce résultat suit l’approche développée pour étudier les processus de branchement uni-variés en environnement aléatoire i. i. d. Il utilise de façon cruciale des résultats récents portant sur les fluctuations des normes de produits de matrices aléatoires i.i.d. / The theory of multi-type branching process in i.i.d. environment is considerably less developed than for the univariate case, and fundamental questions are up to date unsolved. Answers demand a solid understanding of the behavior of products of i.i.d. matrices with non-negative entries. Under mild assumptions, when the probability generating functions of the reproduction laws are fractional-linear, the survival probability of the multi-type branching process in random environment up to moment n is proportional to 1/√n as n → ∞. Techniques for univariate branching process in random environment and methods from the theory of products of i.i.d. random matrices are required.

In this thesis, the structural model in credit risk and the credit derivatives is studied under both Black-Scholes setting and Variance Gamma (VG) setting. Using a Variance Gamma process, the distribution of the firm value process becomes asymmetric and leptokurtic. Also, the jump structure of VG processes allows random default times of the reference entities. Among structural models, the most emphasis is made on the Black-Cox model by building a relation between the survival probabilities of the Black-Cox model and the value of a binary down and out barrier option. The survival probabilities under VG setting are calculated via a Partial Integro Differential Equation (PIDE). Some applications of binary down and out barrier options, default probabilities and Credit Default Swap par spreads are also illustrated in this study.

Made available in DSpace on 2015-03-03T15:32:44Z (GMT). No. of bitstreams: 1 AnnaRSM_DISSERT.pdf: 991497 bytes, checksum: 8cd89e56b698033013c824b49f639a4e (MD5) Previous issue date: 2014-01-30 / We present a dependent risk model to describe the surplus of an insurance portfolio, based on the article "A ruin model with dependence between claim sizes and claim intervals"(Albrecher and Boxma [1]). An exact expression for the Laplace transform of the survival function of the surplus is derived. The results obtained are illustrated by several numerical examples and the case when we ignore the dependence structure present in the model is investigated. For the phase type claim sizes, we study by the survival probability, considering this is a class of distributions computationally tractable and more general / Neste trabalho apresentamos um modelo de risco dependente para descrever o excedente de uma carteira de seguros, com base no artigo "A ruin model with dependence between claim sizes and claim intervals"(Albrecher e Boxma [1]). Obtemos uma express?o exata para a probabilidade de sobreviv?ncia atrav es da Transformada de Laplace da fun??o de sobreviv?ncia do superavit. Ilustramos os resultados obtidos atrav?s de exemplos num?ricos e investigamos o que acontece ao se ignorar a estrutura de depend?ncia presente no modelo. Estudamos tamb?m a probabilidade de sobreviv?ncia para indeniza??es que possuem distribui??o do Tipo Fase, considerando que esta ? uma classe de distribui??es, computacionalmente trataveis, bem mais geral

In this thesis we design and develop algorithms for predicting the rheological behavior of polymer melts based on the results of detailed atomistic simulations and guided by theories of the Dynamics of Polymers and fundamental Principles of Science of the Non-Equilibrium Thermodynamics. More specifically: 1) We propose a new rheological constitutive model for the time evolution of the tensor conformation tensor C of chains in a polymer melt (and hence the stress tensor τ) using the generalized bracket formalism of Beris and Edwards. The new constitutive model includes terms that describe a whole range of phenomena and are successfully used to describe the rheological properties of commercial polyethylene resins. 2) We developed a new methodology that allows direct connection of the results of atomistic simulations with molecular reptation theory for entangled polymers. The final result of the methodology is the calculation of the function ψ(s,t) which expresses the probability that the segment s along the contour of the primitive path remain in the original tube after time t. 3) We extended the Rouse theory for systems without polymer chain ends, as the polymer rings. While there have been previous theoretical work, a comprehensive analysis of the Rouse model of cyclic polymers was still lacking; here we develop the theory in its entirety. / Στα πλαίσια της παρούσας διατριβής σχεδιάσαμε και αναπτύξαμε αλγορίθμους πρόβλεψης της ρεολογικής συμπεριφοράς πολυμερικών τηγμάτων βασιζόμενοι στα αποτελέσματα λεπτομερών ατομιστικών προσομοιώσεων, καθοδηγούμενοι όμως από Θεωρίες της Δυναμικής των Πολυμερών αλλά και από θεμελιώδεις αρχές της Επιστήμης της Θερμοδυναμικής Εκτός Ισορροπίας. Πιο συγκεκριμένα: 1) Προτείνουμε αρχικά ένα νέο ρεολογικό καταστατικό μοντέλο για τη χρονική εξέλιξη του τανυστή διαμορφώσεων C των αλυσίδων σε ένα πολυμερικό τήγμα (και κατ’ επέκταση για τον τανυστή των τάσεων τ) κάνοντας χρήση του φορμαλισμού των γενικευμένων αγκυλών των Beris και Edwards. Το νέο καταστατικό μοντέλο περιλαμβάνει όρους που περιγράφουν ένα ολόκληρο φάσμα φαινομένων και χρησιμοποιήθηκε με επιτυχία για την περιγραφή των ρεολογικών ιδιοτήτων εμπορικών ρητινών πολυαιθυλενίου. 2) Αναπτύξαμε μια καινούργια μεθοδολογία που επιτρέπει την άμεση σύνδεση των αποτελεσμάτων των ατομιστικών προσομοιώσεων με τη μοριακή θεωρία του ερπυσμού για διαπλεγμένα πολυμερή. Το τελικό αποτέλεσμα της μεθοδολογίας είναι ο υπολογισμός της συνάρτησης ψ(s,t) που εκφράζει την πιθανότητα το σημείο s κατά μήκος του περιγράμματος του πρωτογενούς δρόμου των αλυσίδων να παραμένει στον αρχικό σωλήνα μετά από χρόνο t. Επεκτείναμε τη θεωρία Rouse και για συστήματα πολυμερικών αλυσίδων δίχως άκρα, όπως αυτά των πολυμερικών δακτυλίων. Παρότι στίγματα της θεωρίας είχαν παρουσιαστεί και σε προηγούμενες εργασίες από άλλους ερευνητές, στην παρούσα διατριβή αναπτύξαμε τη θεωρία στην ολότητά της.