Graduate Theses & Dissertations

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Positive Solutions for Boundary Value Problems of Second Order Ordinary Differential Equations
In this thesis, we study modelling with non-linear ordinary differential equations, and the existence of positive solutions for Boundary Value Problems (BVPs). These problems have wide applications in many areas. The focus is on the extensions of previous work done on non-linear second-order differential equations with boundary conditions involving first-order derivative. The contribution of this thesis has four folds. First, using a fixed point theorem on order intervals, the existence of a positive solution on an interval for a non-local boundary value problem is obtained. Second, considering a different boundary value problem that consists of the first-order derivative in the non-linear term, an increasing solution is obtained by applying the Krasnoselskii-Guo fixed point theorem. Third, the existence of two solutions, one solution and no solution for a BVP is proved by using fixed point index and iteration methods. Last, the results of Green's function unify some methods in studying the existence of positive solutions for BVPs of nonlinear differential equations. Examples are presented to illustrate the applications of our results. Author Keywords: Banach Space, Boundary Value Problems, Differential Equations, Fixed Point, Norm, Positive Solutions
An Ethical Analysis of Bell's Targeted Ad Prorgram
Online behavioural advertising (OBA) is an advertising technique which relies on collected customer information and online activity to serve people with more relevant ads. On November 16th, 2013, Bell Canada launched their first OBA program via Bell Mobility: the Bell Targeted Ads Program, or BTAP. My thesis provides an ethical analysis of BTAP and shows that Bell undermined and violated customer privacy, stifled customer autonomy, and harmed customer identity. Relevant moral problems include typification, a disrespecting of customer autonomy, and identity commodification. I show that BTAP was unethical by grounding my arguments within the moral framework of Information Ethics (IE). IE is an ethical system which focuses on the role of information in the ethical dilemmas. IE also justifies the self-constitutive theory of privacy (SCP) which argues that our information and privacy are entangled with our identities. This gives us strong reason to defend our privacy/identity within BTAP. After making several arguments which demonstrate that BTAP was unethical, I will then turn my attention to showing how it is possible to rectify and mitigate many of BTAP’s ethical problems by installing a two-stage opt-in (TSOI) which provides customers with a greater deal of autonomy, and the ability to remove themselves from BTAP. Author Keywords: Bell Canada, Ethics, Identity, Online Behavioural Advertising, Privacy, Targeted Advertising
Range-Based Component Models for Conditional Volatility and Dynamic Correlations
Volatility modelling is an important task in the financial markets. This paper first evaluates the range-based DCC-CARR model of Chou et al. (2009) in modelling larger systems of assets, vis-à-vis the traditional return-based DCC-GARCH. Extending Colacito, Engle and Ghysels (2011), range-based volatility specifications are then employed in the first-stage of DCC-MIDAS conditional covariance estimation, including the CARR model of Chou et al. (2005). A range-based analog to the GARCH-MIDAS model of Engle, Ghysels and Sohn (2013) is also proposed and tested - which decomposes volatility into short- and long-run components and corrects for microstructure biases inherent to high-frequency price-range data. Estimator forecasts are evaluated and compared in a minimum-variance portfolio allocation experiment following the methodology of Engle and Colacito (2006). Some consistent inferences are drawn from the results, supporting the models proposed here as empirically relevant alternatives. Range-based DCC-MIDAS estimates produce efficiency gains over DCC-CARR which increase with portfolio size. Author Keywords: asset allocation, DCC MIDAS, dynamic correlations, forecasting, portfolio risk management, volatility
Agro-Ecological Zoning (AEZ) of Southern Ontario and the Projected Shifts Caused by Climate Change in the Long-term Future
This thesis proposes an agro-ecological zoning (AEZ) methodology of southern Ontario for the characterization and mapping of agro-ecological zones during the historical term (1981-2010), and their shifts into the long-term (2041-2070) projected climate period. Agro-ecological zones are homogenous areas with a unique combination of climate, soil, and landscape features that are important for crop growth. Future climate variables were derived from Earth System Models (EMSs) using a high emission climate forcing scenario from the Intergovernmental Panel on Climate Change 5th Assessment Report. The spatiotemporal shifts in agro-ecological zones with projected climate change are analyzed using the changes to the length of growing period (LGP) and crop heat units (CHU), and their manifestation in agro-climatic zones (ACZ). There are significant increases to the LGP and CHU into the long-term future. Two historical ACZs exist in the long-term future, and have decreased in area and shifted northward from their historical locations. Author Keywords: Agro-climatic Zones, Agro-ecological Zones, Agro-ecological Zoning, Climate Change, Crop Heat Units, Length of Growing Period
Disability-Mitigating Effects of Education on Post-Injury Employment Dynamics
Using data drawn from the Workplace Safety and Insurance Board’s (WSIB) Survey of Workers with Permanent Impairments, this thesis explores if and how the human capital associated with education mitigates the realized work-disabling effects of permanent physical injury. Using Cater’s (2000) model of post-injury adaptive behaviour and employment dynamics as the structural, theoretical, and interpretative framework, this thesis jointly studies, by injury type, the effects of education on both the post-injury probability of transitioning from non-employment into employment and the post-injury probability of remaining in employment once employed. The results generally show that, for a given injury type, other things being equal, higher levels of education are associated with higher probabilities of both obtaining and sustaining employment. Author Keywords: permanent impairment, permanent injury, post-injury employment
Long-term Financial Sustainability of China's Urban Basic Pension System
Population aging has become a worldwide concern since the nineteenth century. The decrease in birth rate and the increase in life expectancy will make China’s population age rapidly. If the growth rate of the number of workers is less than that of the number of retirees, in the long run, there will be fewer workers per retiree. This will apply great pressure to China’s public pension system in the next several decades. This is a global problem known as the “pension crisis”. In this thesis, a long-term vision for China’s urban pension system is presented. Based on the mathematical models and the projections for demographic variables, economic variables and pension scheme variables, we test how the changes in key variables affect the balances of the pension fund in the next 27 years. This thesis applies methods of deterministic and stochastic modeling as well as sensitivity analysis to the problem. Using sensitivity analysis, we find that the pension fund balance is highly sensitive to the changes in retirement age compared with other key variables. Monte Carlo simulations are also used to find the possible distributions of the pension fund balance by the end of the projection period. Finally, according to my analysis, several changes in retirement age are recommended in order to maintain the sustainability of China’s urban basic pension scheme. Author Keywords: China, demographic changes, Monte Carlo simulation, pension fund, sensitivity tests, sustainability
Machine Learning Using Topology Signatures For Associative Memory
This thesis presents a technique to produce signatures from topologies generated by the Growing Neural Gas algorithm. The generated signatures have the following characteristics: The signature's memory footprint is smaller than the "real object" and it represents a point in the n x m multidimensional space. Signatures can be compared based on Euclidean distance and distances between signatures provide measurements of differences between models. Signatures can be associated with a concept and then be used as a learning step for a classification algorithm. The signatures are normalized and vectorized to be used in a multidimensional space clustering. Although the technique is generic in essence, it was tested by classifying alphabet and numerical handwritten characters and 2D figures obtaining a good accuracy and precision. It can be used for many other purposes related to shapes and abstract typologies classification and associative memory. Future work could incorporate other classifiers. Author Keywords: Associative memory, Character recognition, Machine learning, Neural gas, Topological signatures, Unsupervised learning
Utilizing Class-Specific Thresholds Discovered by Outlier Detection
We investigated if the performance of selected supervised machine-learning techniques could be improved by combining univariate outlier-detection techniques and machine-learning methods. We developed a framework to discover class-specific thresholds in class probability estimates using univariate outlier detection and proposed two novel techniques to utilize these class-specific thresholds. These proposed techniques were applied to various data sets and the results were evaluated. Our experimental results suggest that some of our techniques may improve recall in the base learner. Additional results suggest that one technique may produce higher accuracy and precision than AdaBoost.M1, while another may produce higher recall. Finally, our results suggest that we can achieve higher accuracy, precision, or recall when AdaBoost.M1 fails to produce higher metric values than the base learner. Author Keywords: AdaBoost, Boosting, Classification, Class-Specific Thresholds, Machine Learning, Outliers
Application of One-factor Models for Prices of Crops and Option Pricing Process
This thesis is intended to support dependent-on-crops farmers to hedge the price risks of their crops. Firstly, we applied one-factor model, which incorporated a deterministic function and a stochastic process, to predict the future prices of crops (soybean). A discrete form was employed for one-month-ahead prediction. For general prediction, de-trending and de-cyclicality were used to remove the deterministic function. Three candidate stochastic differential equations (SDEs) were chosen to simulate the stochastic process; they are mean-reverting Ornstein-Uhlenbeck (OU) process, OU process with zero mean, and Brownian motion with a drift. Least squares methods and maximum likelihood were used to estimate the parameters. Results indicated that one-factor model worked well for soybean prices. Meanwhile, we provided a two-factor model as an alternative model and it also performed well in this case. In the second main part, a zero-cost option package was introduced and we theoretically analyzed the process of hedging. In the last part, option premiums obtained based on one-factor model could be compared to those obtained from Black-Scholes model, thus we could see the differences and similarities which suggested that the deterministic function especially the cyclicality played an essential role for the soybean price, thus the one-factor model in this case was more suitable than Black-Scholes model for the underlying asset. Author Keywords: Brownian motion, Least Squares Method, Maximum Likelihood Method, One-factor Model, Option Pricing, Ornstein-Uhlenbeck Process
Modeling drought derivatives in arid regions
We propose a stochastic weather model based on temperature, precipitation, humidity and wind speed for Qatar, as a representative arid region, in order to obtain simulated values for a drought index. As a drought index, the Reconnaissance Drought Index (RDI) is commonly accepted in agriculture and is used to measure drought severity. It can be used to price weather derivatives to help farmers reduce nancial losses from drought. RDI, which is the ratio of precipitation to evapotranspiration, is calculated by considering crop growth stages. The use of dierent crop coecient value depending on the growth stage to calculate evapotranspiration can provide improved values for RDI. Additionally, six calculation methods for evapotranspiration using weather data are investigated to obtain accurate values for RDI. Author Keywords: Evapotranspiration, Markov chains, Mean reversion processes, Reconnaissance Drought Index, Stochastic dierential equations, Stochastic weather models
Effect of Listing a Stock on the S&P 500 Index on the Stock’s Volatility
This paper investigates the effect of listing a stock on the S&P 500 Index on the stock’s volatility, using various econometrics models: GARCH and EGARCH. The study mainly addresses three issues; firstly, it analyzes stock volatility in two sub-periods, secondly, it determines whether the announcement can account for the fluctuations in the price of the stock, and finally, it investigates the change in the stock’s variance. After isolating the effects of external and industry shock by using the returns on the S&P 500 Index as a proxy, the author finds evidence of structural change in the volatility of stocks after that stock is added to the index. Additionally, the existence of a dominant symmetric effect, which captures the response of volatility to news, indicate that following the onset of including the stock on the index, information flowing into the market increased. However, the rate at which old news is captured in price falls. The empirical evidence also suggests that on average a stocks variance falls and that the announcement to list a stock on the index has little effect on the stock’s price. Author Keywords: EGARCH, GARCH, S&P 500 Index, Symmetric Effect, Volatility
Smote and Performance Measures for Machine Learning Applied to Real-Time Bidding
In the context of Real-Time Bidding (RTB) the machine learning problems of imbalanced classes and model selection are investigated. Synthetic Minority Oversampling Technique (SMOTE) is commonly used to combat imbalanced classes but a shortcoming is identified. Use of a distance threshold is identified as a solution and testing in a live RTB environment shows significant improvement. For model selection, the statistical measure Critical Success Index (CSI) is modified to add emphasis on recall. This new measure (CSI-R) is empirically compared with other measures such as accuracy, lift, efficiency, true skill score, Heidke's skill score and Gilbert's skill score. In all cases CSI-R is shown to provide better application to the RTB industry. Author Keywords: imbalanced classes, machine learning, online advertising, performance measures, real-time bidding, SMOTE

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Graduate student theses produced at Trent University. You may also browse theses and dissertations by year, program, or author.

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