This thesis examines finite dimensional representability of Forward Rate and LIBOR models. A new approach is examined. This approach is more general, elementary, and relevant to finance when compared with existing approaches. This new approach is applied to the following infinite dimensional equations used in finance: ?Gaussian Heath, Jarrow and Morton model; ?Free 1 Heath, Jarrow and Morton model; ?Brace, G?atarek and Musiela???s LIBOR model. Stronger results have been achieved using this approach. The results are as follows: ?The Gaussian HJM model can be represented in finite dimensions if and only if the volatility satisfies a particular differential equation. In which case the finite dimensional representation can be explicitly written; ?The Brace, G?atarek and Musiela???s LIBOR model with one dimensional Wiener process cannot be represented in finite dimensions (other than in a trivial case); ?The Brace, G?atarek and Musiela???s LIBOR model with multidimen-sional Wiener process, and Free HJM have a finite dimensional repre-sentation only if the initial yield curves satisfy a restrictive differential equation. This thesis is arranged as follows ?Chapter 1 is an introduction to this thesis and derivative pricing in general. The reader is referred to section 1.4 titled ???This Thesis?for a more detailed description of the approach of this thesis and its results. ?Chapter 2 contains a brief summary of results from the theory of stochastic processes, stochastic calculus and stochastic equations in infinite dimensions ?Chapter 3 contains an overview of spot market pricing models including the Cox, Ross and Rubinstein and Black and Scholes models. ?Chapter 4 contains an overview of the fixed income market pricing models including the Heath, Jarrow and Morton model; Musiela???s re-formulation of the HJM model; the Goldys, Musiela and Sondermann model; and the Brace, G?atarek and Musiela LIBOR model. ?Chapter 5 contains the primary results of this thesis. Finite Dimen-sional Representability is defined formally and applied to the Musiela reformulated Gaussian HJM model; Musiela reformulated free HJM model; and the Brace, G?atarek and Musiela LIBOR model. This ap-proach and results are compared with the literature.

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Zugl.: Darmstadt, Techn. Univ., Diss., 2006

<p>The customers perceived all 5 SERVQUAL dimensions; tangibles, reliability, assurance, responstiveness, and empathy, pertaining service quality performance at low level when compared with their expectation. Thailand Resor AB should fulfill these 5 gaps and pay attention at assurance dimension concerning conveying trust and confidence because of the highest gap. The dimension of tangibles (equipment, physical facilities, etc.), empathy (ability to see through the customer’s eyes), responstiveness (willingness to help and provide prompt service), and reliability (doing what company have promised) were adjusted consequencely. The respondents highlighted the following key quality factors of their expectations; be treated with respect, be listened to and be dedicated attention, more friendly staffs, get the accoracy information. Some respondent have fuzzy expectations that he company have to further discover the real expectations by providing gauidance to their staffs to encourage them to ask questions.</p>

In this thesis, we study the mathematical modelling of some problems that involve surface effects. These include an optical biosensor, which uses optical principles qualitatively to convert chemical and biochemical concentrations into electrical signals. A typical sensor of this type was constructed in Badley et al., [6], and Jones et al., [18],but diffusion was considered in only one direction in [18] to simulate the reaction between the antigen and the antibody. For realistic applications, we propose the biosensor model in R3. Our theoretical approach is explicitly presented since it is simple and directly applicable to the numerical part of the thesis. In particular, we present existence and uniqueness results based on Maximum Principle and weak solution arguments. These ideas are later applied to systems and to the numerical analysis of the approximate discretized problems.It should be noted that without one dimensional symmetry, the equations can not be decoupled in order to reduce the problem to a single equation. We also show the long time monotonic convergence to the steady state. Next, a finite volume method is applied to the equations, and we obtain existence and uniqueness for the approximate solution as well as the convergence of the the first order temporal norm and the L2 spatial norm. We illustrate the results via some numerical simulations. Finally we consider a mathematically related system motivated by lagoon ecology. We show that under suitable conditions on the coecients, the system has a periodic solution under harvesting conditions. The mathematical techniques now depend on estimates for periodic parabolic problems. / Applied Mathematics

Steel plate shear walls have typically been analyzed using quasi static and monotonic pushover analysis; however, dynamic excitations during an earthquake elicit different behaviour from the structure due to the nature of the loading. This report outlines the design and analysis of a steel plate shear wall according to NBCC and S16-09 requirements. For lateral loading, wind and seismic forces are considered. The NBCC recognizes two procedures for determining seismic loading, the equivalent static force procedure and dynamic analysis. An analytical model was created in SAP2000® using capacity design principals and the strip model. The dynamic analysis uses bi-directional tension strips to resist load reversals and was validated against a finite element analysis using ABAQUS®. The dynamic analysis provided an effective means of designing the steel plate shear wall. The equivalent static force procedure resulted in a similar design; however, the structure required stiffening to meet the deflection requirements.

Suicide is one of the most tragic issues in mental health. Suicide has traditionally been studied as an outcome of specific psychiatric disorders. The goal of this study was to consider whether there might be underlying dimensions across psychiatric disorders that are related to suicidality. This study proposed a transdiagnostic model of suicidality. Psychiatric symptoms were hypothesized to load onto three factors: Negative Mood, Impulsivity, and Arousal. Factors were then examined as predictors of suicidal ideation and suicide attempts. Data were drawn from the National Comorbidity Survey-Replication Study (NCS-R). Structured interviews were conducted in two parts using the Composite International Diagnostic Interview (CIDI). All survey respondents (N = 9,282) were administered the core diagnostic assessment. Those who met criteria for a psychiatric disorder, met subthreshold lifetime criteria and sought treatment at some time in their life, or ever in their life made a plan to commit or attempt suicide were administered Part II of the interview and are the sample of interest in this study (N = 5,692). The sample was representative of non-institutionalized civilian adults ages 18 or older whose primary language was English. Factor analyses revealed three modified factors: a Negative Mood/Emotional Arousal factor, a Negative Thinking factor, and a Recurrent Substance Use factor. Negative Mood/Emotional Arousal was a strong predictor of suicidal ideation. Suicidal ideation mediated the relationship between Negative Mood/Emotional Arousal and suicide attempts, controlling for Negative Thinking. Negative Thinking, Recurrent Substance Use, and suicidal ideation predicted suicide attempts. When number of suicide attempts was examined as the dependent variable, the model did not fit the data, suggesting that these factors were not as helpful in predicting highly recurrent suicide attempts. Recurrent Substance Use moderated the relationship between Negative Mood/Emotional Arousal and suicide attempts, demonstrating that, as negative mood increases, people with high levels of recurrent substance use are more likely to make a suicide attempt compared to people with mean or low levels of recurrent substance use. In sum, results of this study support two distinct pathways to making a suicide attempt: a direct relationship between negative thinking and suicide attempts, as well as an interaction between negative mood/emotional arousal and recurrent substance use. Several limitations including issues of sampling, the cross-sectional nature of the data, self-report bias, and the structure of the CIDI instrument, were taken into account in interpreting the results. Clinical implications and future directions for research are discussed.

This research consists of two parts. The first part examines the posterior probability integrals for a family of linear models which arises from the work of Hart, Koen and Lombard (2003). Applying Laplace's method to these integrals is not entirely straightforward. One of the requirements is to analyze the asymptotic behavior of the information matrices as the sample size tends to infinity. This requires a number of analytic tricks, including viewing our covariance matrices as tending to differential operators. The use of differential operators and their Green's functions can provide a convenient and systematic method to asymptotically invert the covariance matrices. Once we have found the asymptotic behavior of the information matrices, we will see that in most cases BIC provides a reasonable approximation to the log of the posterior probability and Laplace's method gives more terms in the expansion and hence provides a slightly better approximation. In other cases, a number of pathologies will arise. We will see that in one case, BIC does not provide an asymptotically consistent estimate of the posterior probability; however, the more general Laplace's method will provide such an estimate. In another case, we will see that a naive application of Laplace's method will give a misleading answer and Laplace's method must be adapted to give the correct answer. The second part uses numerical methods to compute the "exact" posterior probabilities and compare them to the approximations arising from BIC and Laplace's method.

The U.S. wool industry has long received lower prices for comparable wool types than those of Australia. In order to better understand such price differences, economic evaluations of both the U.S. and Australian wool markets were conducted. This research focused on two primary objectives. The first objective was to determine what price differences existed between the Australian and U.S. wool markets and measure that difference. The second objective was to calculate price differences attributable to wool characteristics, as well as those resulting from regional, seasonal, and yearly differences. In order to accomplish the objectives, the study was set up into three different hedonic pricing models: U.S., Australian, and combined. In the U.S. model, there were significant price differences in season, year, region, level of preparation, and wool description. In addition, average fiber diameter (AFD) had a negative nonlinear relationship with price and lot weight had a positive linear relationship with price. The Australian model was notably different than the U.S. model in that there were only three variables. The yearly variable follows the same general pattern as the U.S. data but with a smaller span of difference. The seasonal price differences were distinctly different than the U.S. because of the difference in seasonal patterns. In addition, the AFD had a similar negative nonlinear relationship with price. The final model combines both the U.S. data and the Australian data. The combined model had only three variables: season, year, AFD and country. As in the case of the previous two models, AFD had the same negative nonlinear relationship and similar price elasticity. Overall, there was a -30.5 percent discount for U.S. wool when compared to Australian wool. This can be attributed to several different factors. One of which is that the Australian wool industry has a more extensive marketing scheme when compared to the U.S wool market as a whole. However, this is only a beginning to future research that needs to be conducted. Continuing this study for future years, having more descriptive categories, and additional countries would further add explanation to wool prices.

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