Mathematics & Statistics

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Open Access
Nonlinear Dynamics, Stochastic Methods, And Predictive Modelling For Infectious Disease: Application To Public Health And Epidemic Forecasting
(2025-04-10) Prashad, Christopher Daniel; Wu, Jianhong
Statistical models must adapt to the evolving nature of many processes over time. This thesis introduces flexible models and statistical methods designed to infer data-generating processes that vary temporally. The primary objective is to develop frameworks for efficient estimation and prediction of both univariate and multivariate time series data. The models considered are general dynamic predictive models with parameters that change over time, featuring time-varying regression coefficients or variance components. These models are capable of accommodating time-dependent covariates and can handle situations where information is incomplete. Several novel enhancements to existing mathematical models are introduced, with a particular focus on online learning and real-time prediction. Efficient Bayesian inference methodology is developed for analyzing the posterior of covariance components of dynamic models sequentially with a closed-form estimation algorithm for real-time online processing. Additionally, an online change detection algorithm for structural breaks is developed, combining the benefits of Kalman filters with sequential Monte Carlo methods. A general and extensible compartmental model for the study of infectious disease data is proposed, with several innovative extensions to established probability models for the analysis of data. Next, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model by integrating innovative stochastic mean-reverting transmission processes to more accurately capture the variability observed in real-world epidemic data. Lastly, we provide a methodology that harnesses expansive data sources and feature engineering for analyzing and forecasting peak time and height of epidemic waves, crucial for the planning of public health strategies and interventions. The performance of these inference methodologies is assessed through simulation experiments and real data from clinical, social-demographic, and epidemic domains.
Open Access
Transmission Dynamics And Control Of Cholera In Africa: A Mathematical Modelling Approach
(2025-04-10) Adeniyi, Ebenezer Olayinka; Kong, Jude
Background: Cholera, caused by Vibrio cholerae, is a global health threat, with outbreaks surging since 2021, particularly in Africa. In 2024, over 13 African countries faced outbreaks worsened by climatic events, poverty, and weak healthcare systems. A shortage of vaccines further complicates control efforts. Objective: This study uses data science, machine learning, and modelling to analyze cholera dynamics, identify outbreak drivers, and propose targeted interventions. Methods: A compartmental model with Bayesian estimation analyzed cholera data from eight African countries. Sensitivity analysis identified key transmission parameters, and hierarchical clustering grouped countries by outbreak characteristics. Results: Average R0 was 2.0, ranging from 1.41 (Zimbabwe) to 2.80 (Mozambique). Factors like infection rate and human shedding increased R0, while recovery rate reduced it. Clustering identified three outbreak drivers: natural disasters, conflict, and sanitation issues. Conclusion: Tailored, data-driven interventions are critical for effective cholera management across diverse contexts.
Open Access
Robust Statistical Modeling In Functional Linear Regression
(2025-04-10) Yan Zhang; Wu, Yuehua
Functional linear regression is a prominent field within the domain of functional data analysis, with extensive applications in various domains such as biomedical studies, brain imaging, and chemometrics. However, despite the abundance of literature on functional linear regression, limited attention has been devoted to addressing outliers or heavy-tailed distributions in the data. Consequently, robust statistical analysis remains an underdeveloped practice in this area. The primary objective of this dissertation is to enhance the utilization of robust methods for modeling functional linear regression by primarily focusing on robust estimation techniques, hypothesis testing procedures that are resilient to outliers or heavy-tailed distributions, and robust variable selection methods. First, we consider the problem of robust estimation in partial functional linear models under RKHS framework. The theoretical properties of robust estimation simulation studies are discussed in this chapter. Furthermore, two real data examples are presented to illustrate the performance of the robust procedure. Then, we extend three robust tests: Wald-type, the likelihood ratio-type and F-type in functional linear models. Meanwhile, we investigate the theoretical properties of these robust testing procedures and assess the finite sample properties through the numerical simulation. Finally, we propose a robust variable selection method in multiple functional linear regression and present a novel algorithm for identifying significant functional predictors using a robust group variable inflation factor (VIF) selection procedure. Our methodology is validated through rigorous simulation studies as well as its application to real-world data. To ensure the cohesiveness of this dissertation, Chapter 1 provides an introduction to the research background, mathematical foundations, and primary motivations underlying this study. Chapter 2 presents a comprehensive overview of basis expansion methods for functional data analysis. Lastly, Chapter 6 concludes this dissertation by offering potential avenues for future research.
Open Access
On PCF Polynomials
(2025-04-10) Fraser, Benjamin Alexander; Ingram, Patrick
The author of [27] proves that the set of post-critically finite (PCF) polynomials of given degree is a set of bounded height, up to PGL_2-conjugacy. This result is extended to show that the set of monic polynomials g(z) with rational coefficients of given degree such that there exists a d ≥ 2 such that g(z^d) is PCF, is also a set of bounded height. Note that by fixing the degree of a polynomial and algebraic degree of its coefficients, the set of such PCF polynomials is in fact finite, and computable. Bounds on the coefficients for quartic PCF polynomials with rational coefficients are computed, and a search of the resulting space yields 16 distinct conjugacy classes. Infinite families of PCF polynomials containing each of these distinct conjugacy classes are found, giving a lower bound on the number of such conjugacy classes in terms of degree d.
Open Access
The Mathematics Of Deep Neural Networks With Application In Predicting The Spread Of Infectious Diseases Through Disease Informed Neural Networks (DINNs)
(2025-04-10) Golooba, Nickson; Woldegerima, Woldegebriel Assefa
Deep learning has emerged in many fields in recent times where neural networks are used to learn and understand data. This thesis combines deep learning frameworks with epidemiological models and is aimed specifically at the creation and testing of DINNs with a view to modeling the infection dynamics of epidemics. This research thus trains the DINN on synthetic data derived from an SI-SIR model designed for Avian influenza and shows the model’s accuracy in predicting extinction and persistence conditions. In the method, a twelve hidden layer model was constructed with sixty-four neurons per layer and ReLU activation function was used. The network is trained to predict the time evolution of five state variables for birds and humans over 50,000 epochs. The overall loss minimized to 0.000006, was characterized of the loss of data and physics, which made the DINN follow the differential equations that fundamentally described the disease progression.
Open Access
Investigating The Plethysm Coefficients For Schur Functions
(2025-04-10) Tatsinkou Tenekeu, Roosvel; Zabrocki, Mike
Plethysm is an operation on symmetric functions, which is important in representation theory and algebraic combinatorics. However, efficient methods for finding the coefficients that emerge when plethysms of Schur functions are expanded using the Schur basis remain a challenge. The main goal of this thesis is to explore and suggest solutions to the problem of determining plethysm coefficients. This study aims to introduce methods for computing these plethysm coefficients, offering formulas where feasible and investigating their combinatorial and algebraic characteristics. This research seeks to employ theoretical and computational tools analysis to enhance our comprehension of plethysm and contribute to the wider domain of symmetric function theory.
Open Access
Algebra Structure On Set Partitions
(2025-04-10) Solomon, Yohana; Zabrocki, Mike
The partition algebra is an algebra with a basis of set partitions diagrams. Its subalgebra includes diagram algebras such as the uniform block permutations and the group algebra of the symmetric group. We connect the Hopf algebra of uniform block permutations to the diagram algebra known as the party algebra. This is done by describing a new basis of the partition algebra and looking at the relationship to the basis given for the Hopf algebra of uniform block permutations. The product and coproduct of the Hopf algebra of uniform block permutations are the generalization of the product of the Malvenuto-Reutenauer Hopf algebra of permutations. We connect the product of the uniform block permutations with the bases of the partition algebra. The centralizer algebra has an internal product and we define an external product on the partition algebra. This algebra contains the algebra of uniform block permutations and the algebra of permutations.
Open Access
Selected Computational Problems In Insurance
(2025-04-10) Fleck, Andrew; Furman, Edward
The coming together of digital data sets, computational power and rigorous probability theory has transformed finance and insurance in the last century. Once the purview of heuristics and an almost artisanal knowledge, these fields have increasingly taken on a scientific sophistication in technique. Modern regulations even require firms to retain the mathematical skill necessary to perform complex risk analysis. Mechanical heuristics originally developed in the absence of probabilistic assumptions have been demystified and reworked for novel applications. Complex structured products can be simulated and statistical learning algorithms can be applied to gain insights where none existed before. This dissertation is concerned with such problems. In the realm of property and casualty insurance, this thesis addresses challenges in risk estimation, quantification and allocation when the risk can be modelled by multivariate Stable distributions, which we will argue provide a suitable null model in the case of heavy-tailed losses. Traditionally the lack of means and distribution functions has rendered these distributions difficult to work with. We will sidestep this issue in estimation by using an integral transformation-based method of estimation. For risk quantification, we develop computationally simple and efficient representations of commonly used risk measures. Allocation then follows from our choice of dependence structure. In the area of life contingencies, we will study a relatively new product, the fixed index annuity (FIA). The variety of annuity parameters and the complexity of the underlying index make FIA comparisons very challenging. While still an insurance product, FIAs require sophisticated models of equity indices to analyze. We elect to use machine learning techniques to reproduce FIA-linked equity indices. In order to understand our often surprising results, we make use of a few stochastic volatility models.
Open Access
Multiple Risk Factors Dependence Structures With Applications to Actuarial Risk Management
(2024-11-07) Su, Jianxi; Furman, Edward
Actuarial and financial risk management is one of the most important innovations of the 20th century, and modelling dependent risks is one of its central issues. Traditional insurance models build on the assumption of independence of risks. Criticized as one of the main causes of the recent financial crisis, this assumption has facilitated the quantification of risks for decades, but it has often lead to under-estimation of the risks and as a result under-pricing. Hence importantly, one of the prime pillars of the novel concept of Enterprise Risk Management is the requirement that insurance companies have a clear understanding of the various interconnections that exist within risk portfolios. Modelling dependence is not an easy call. In fact, there is only one way to formulate independence, whereas the shapes of stochastic dependence are infinite. In this dissertation, we aim at developing interpretable practically and tractable technically probabilistic models of dependence that describe the adverse effects of multiple risk drivers on the risk portfolio of a generic insurer. To this end, we introduce a new class of Multiple Risk Factor (MRF) dependence structures. The MRF distributions are of importance to actuaries through their connections to the popular frailty models, as well as because of the capacity to describe dependent heavy-tailed risks. The new constructions are also linked to the factor models that lay in the very basis of the nowadays financial default measurement practice. Moreover, we use doubly stochastic Poisson processes to explore the class of copula functions that underlie the MRF models. Then, motivated by the asymmetric nature of these copulas, we propose and study a new notion of the paths of maximal dependence, which is consequently employed to measure tail dependence in copulas.
Open Access
Results about Proximal and Semi-proximal Spaces
(2024-07-18) Almontashery, Khulod Ali M.; Szeptycki, Paul J.
Proximal spaces were defined by J. Bell as those topological spaces $X$ with a compatible uniformity ${\mathfrak U}$ on which Player I has a winning strategy in the so-called proximal on $(X,{\mathfrak U})$. Nyikos defined the class of semi-proximal spaces where Player II has no winning strategy on $(X,{\mathfrak U})$ with respect to some compatible uniformity. The primary focus of this thesis is to study the relationship between the classes of semi-proximal spaces and normal spaces. Nyikos asked whether semi-proximal spaces are always normal. The main result of this thesis is the construction of two counterexamples to this question. We also examine the characterization of normality in subspaces of products of ordinals, relating it to the class of semi-proximal spaces in finite power of $\omega_1$. In addition, we introduce a strengthening of these classes by restricting the proximal game to totally bounded uniformities. We study connections between the proximal game, the Galvin game, and the Gruenhage game. Further, we explore the relationship between semi-proximality and other convergence properties.
Open Access
Polarization Operators in Superspace
(2024-07-18) Chan, Kelvin Tian Yi; Bergeron, Nantel
The classical coinvariant rings and its variants are quotient rings with rich connections to combinatorics, symmetric function theory and geometry. Studies of a generalization of the classical coinvariant rings known as the diagonal harmonics have fruitfully produced many interesting discoveries in combinatorics including the q, t-Catalan numbers and the Shuffle Theorem. The super coinvariant rings are a direct generalization of the classical coinvariant rings to one set of commuting variables and one set of anticommuting variables. N. Bergeron, Li, Machacek, Sulzgruber, and Zabrocki conjectured in 2018 that the super coinvariant rings are representation theoretic models for the Delta Conjecture at t = 0. In this dissertation, we explore the super coinvariant rings using algebraic and combina- torial methods. In particular, we study the alternating component of the super harmonics and discover a novel basis using polarization operators. We use polarization equivalence to establish a triangularity relation between the new basis and a known basis due to two groups of researchers Bergeron, Li, Machacek, Sulzgruber, and Zabrocki and Swanson and Wallach. Furthermore, we prove a folklore result on the cocharge statistics of standard Young tableaux and propose a basis for every irreducible representation appearing in the super harmonics.
Open Access
One-Parameter Semigroups Generated by Strongly M-Elliptic Pseudo-Differential Operators on Euclidean Spaces
(2024-07-18) Gao, Yaodong; Wong, Man Wah
We begin with a recall of the definitions and basic properties of the standard Hörmander classes of pseudo-differential operators on Rn. Then we introduce a new class of pseudo-differential operators that can be traced back to Taylor, generalized by Garello and Morando and further developed by M. W. Wong. A related class of pseudo-differential operators depending on a complex parameter on an open subset of the complex plane is constructed. We tease out from this related class the strongly M – elliptic pseudo-differential operators and prove that they are infinitesimal generators of holomorphic and hence strongly continuous one-parameter semigroups of bounded linear operators on Lp(Rn), 1
Open Access
A High-Order Navier-Stokes Solver for Viscous Toroidal Flows
(2024-03-16) Siewnarine, Vishal; Haslam, Michael C.
This thesis details our work in the development and testing of highly efficient solvers for the Navier-Stokes problem in simple toroidal coordinates in three spatial dimensions. In particular, the domain of interest in this work is the region occupied by a fluid between two concentric toroidal shells. The study of this problem was motivated in part by extensions of the study of Taylor-Couette instabilities between rotating cylindrical and spherical shells to toroidal geometries. We note that at higher Reynolds numbers, Taylor-Couette instabilities in cylindrical and spherical coordinates are essentially three dimensional in nature, which motivated us to design fully three-dimensional solvers with a OpenMP parallel numerical implementation suitable for a multi-processor workstation. We approach this problem using two different time stepping procedures applied to the so-called Pressure Poisson formulation of the Navier-Stokes equations. In the first case, we develop an ADI-type method based on a finite difference formulation applicable for low Reynolds number flows. This solver was more of a pilot study of the problem formulated in simple toroidal coordinates. In the second case - the main focus of our thesis - our main goal was to develop a spectral solver using an explicit fourth order Runge-Kutta time stepping, which is appropriate to the higher Reynolds number flows associated with Taylor-Couette instabilities. Our spectral solver was developed using a high order Fourier representation in the angular variables of the problem and a high order Chebyshev representation in the radial coordinate between the shells. The solver exhibits super-algebraic convergence in the number of unknowns retained in the problem. Applied to the Taylor-Couette problem, our solver has allowed us to identify (for the first time, in this thesis) highly-resolved Taylor-Couette instabilities between toroidal shells. As we document in this work, these instabilities take on different configurations, depending on the Reynolds number of the flow and the gap width between shells, but as of now, all of these instabilities are essentially two dimensions. Our work on this subject continues, and we confident that we will uncover three-dimensional instabilities that have well-known analogues in the cases of cylindrical and spherical shells. Lastly, a separate physical problem we examine is the flow between oscillating toroidal shells. Again, our spectral solver is able to resolve these flows to spectral accuracy for various Reynolds numbers and gap widths, showing surprisingly rich physical behaviour. Our code also allows us to document the torque required for the oscillation of the shells, a key metric in engineering applications. This problem was investigated since this configuration was recently proposed as a mechanical damping system.
Open Access
Second-order finite free probability
(2024-03-16) McConnell, Curran; Bergeron, Nantel
Finite free probability is a new field lying at the intersection of random matrix theory and non-commutative probability. It is called “finite” because unlike traditional free probability, which takes the perspective of operators on infinite-dimensional vector spaces, finite free probability focuses on the study of d × d matrices. Both fields study the behaviour of the eigenvalues of random linear transformations under addition. Finite free probability seeks in particular to characterize random matrices in terms of their (random) characteristic polynomials. I studied the covariance between the coefficients of these polynomials, in order to deepen our knowledge of how random characteristic polynomials fluctuate about their expected values. Focusing on a special case related to random unitary matrices, I applied the representation theory of the unitary group to derive a combinatorial summation expression for the covariance.
Open Access
Markov Chains, Clustering, and Reinforcement Learning: Applications in Credit Risk Assessment and Systemic Risk Reduction
(2023-12-08) Le, Richard; Ku, Hyejin
In this dissertation we demonstrate how credit risk assessment using credit rating transition matrices can be improved, as well as present a novel reinforcement learning (RL) model capable of determining a multi-layer financial network configuration with reduced levels of systemic risk. While in this dissertation we treat credit risk and systemic risk independently, credit risk and systemic risk are two sides of the same coin. Financial systems are highly interconnected by their very nature. When a member of this system experiences distress such as default, a credit risk event, this distress is often not felt in isolation. Due to the highly interconnected nature of financial systems, these shocks can spread throughout the system resulting in catastrophic failure, a systemic risk event. The treatment of credit risk begins with the introduction of our first-order Markov model augmented with sequence-based clustering (SBC). Once we established this model, we explored its ability to predict future credit rating transitions, the transition direction of the credit ratings, and the default behaviour of firms using historical credit rating data. Once validated, we then extend this model using higher-order Markov chains. This time around, focusing more on the absorbing behaviour of Markov chains, and hence, the default behaviour under this new model. Using higher-order Markov chains, we also enjoy the benefit of capturing a phenomenon known as rating momentum, characteristic of credit rating transition behaviour. Other than the credit rating data set, this model was also applied to a Web-usage mining data set, highlighting its generalizability. Finally, we shift our focus to the treatment of systemic risk. While methods exist to determine optimal interbank lending configurations, they only treat single-layer networks. This is due to technical optimization challenges that arise when one considers additional layers and the interactions between them. These layers can represent lending products of different maturities. To consider the interaction between layers, we extend the DebtRank (DR) measure to track distress across layers. Next, we develop a constrained deep-deterministic policy gradient (DDPG) model capable of reorganizing the interbank lending network structure, such that the spread of distress is better mitigated.
Open Access
Invisible Frontiers: Robust and Risk-Sensitive Financial Decision-Making within Hidden Regimes
(2023-12-08) Wang, Mingfu; Ku, Hyejin
In this dissertation, we delve into the exploration of robust and risk-sensitive strategies for financial decision-making within hidden regimes, focusing on the effective portfolio management of financial market risks under uncertain market conditions. The study is structured around three pivotal topics, that is, Risk-sensitive Policies for Portfolio Management, Robust Optimal Life Insurance Purchase and Investment-consumption with Regime-switching Alpha-ambiguity Maxmin Utility, and Robust and Risk-sensitive Markov Decision Process with Hidden Regime Rules. In Risk-sensitive policies for Portfolio Management, we propose two novel Reinforcement Learning (RL) models. Tailored specifically for portfolio management, these models align with investors’ risk preference, ensuring the strategies balance between risk and return. In Robust Optimal Life Insurance Purchase and Investment-consumption with Regime-switching Alpha-ambiguity Maxmin Utility, we introduce a pre-commitment strategy that robustly navigates insurance purchasing and investment-consumption decisions. This strategy adeptly accounts for model ambiguity and individual ambiguity aversion within a regime-switching market context. In Robust and Risk-sensitive Markov Decision Process with Hidden Regime Rules, we integrate hidden regimes into Markov Decision Process (MDP) framework, enhancing its capacity to address both market regime shifts and market fluctuations. In addition, we adopt a risk-sensitive objective and construct a risk envelope to portray the worst-case scenario from RL perspective. Overall, this research strives to provide investors with the tools and insights for optimal balance between reward and risk, effective risk management and informed investment choices. The strategies are designed to guide investors in the face of market uncertainties and risk, further underscoring the criticality of robust and risk-sensitive financial decision-making.
Open Access
On Laplace transforms, generalized gamma convolutions, and their applications in risk aggregation
(2023-12-08) Miles, Justin Christopher; Kuznetsov, Alexey
This dissertation begins with two introductory chapters to provide some relevant background information: an introduction on the Laplace transform and an introduction on Generalized Gamma Convolutions (GGCs). The heart of this dissertation is the final three chapters comprised of three contributions to the literature. In Chapter 3, we study the analytical properties of the Laplace transform of the log-normal distribution. Two integral expressions for the analytic continuation of the Laplace transform of the log-normal distribution are provided, one of which takes the form of a Mellin-Barnes integral. As a corollary, we obtain an integral expression for the characteristic function; we show that the integral expression derived by Leipnik in \cite{Leipnik1991} is incorrect. We present two approximations for the Laplace transform of the log-normal distribution, both valid in $\C \setminus(-\infty,0]$. In the last section, we discuss how one may use our results to compute the density of a sum of independent log-normal random variables. In Chapter 4, we explore the topic of risk aggregation with moment matching \\approximations. We put forward a refined moment matching approximation (MMA) method for approximating the distributions of the sums of insurance risks. Our method approximates the distributions of interest to any desired precision, works equally well for light and heavy-tailed distributions, and is reasonably fast irrespective of the number of the involved summands. In Chapter 5, we study the convergence of the Gaver-Stehfest algorithm. The Gaver-Stehfest algorithm is widely used for numerical inversion of Laplace transform. In this chapter we provide the first rigorous study of the rate of convergence of the Gaver-Stehfest algorithm. We prove that the Gaver-Stehfest approximations of order $n$ converge exponentially fast if the target function is analytic in a neighbourhood of a point and they converge at a rate $o(n^{-k})$ if the target function is $(2k+3)$-times differentiable at a point.
Open Access
Mathematical and Statistical Analysis of Non-stationary Time Series Data
(2023-12-08) Hang, Du; Wang, Steven
Non-stationary time series, with intrinsic properties constantly changing over time, present significant challenges for analysis in various scientific fields, particularly in biomedical signal analysis. This dissertation presents novel methodologies for analyzing and classifying highly noisy and non-stationary signals with applications to electroencephalograms (EEGs) and electrocardiograms (ECGs). The first part of the dissertation focuses on a framework integrating pseudo-differential operators with convolutional neural networks (CNNs). We present their synergistic potential for signal classification from an innovative perspective. Building on the fundamental concept of pseudo-differential operators, the dissertation further proposes a novel methodology that addresses the challenges of applying time-variant filters or transforms to non-stationary signals. This approach enables the neural network to learn a convolution kernel that changes over time or location, providing a refined strategy to effectively handle these dynamic signals. This dissertation also introduces a hybrid convolutional neural network that integrates both complex-valued and real-valued components with the discrete Fourier transform (DFT) for EEG signal classification. This fusion of techniques significantly enhances the neural network's ability to utilize the phase information contained in the DFT, resulting in substantial accuracy improvements for EEG signal classification. In the final part of this dissertation, we apply a conventional machine learning approach for the detection and localization of myocardial infarctions (MIs) in electrocardiograms (ECGs) and vectorcardiograms (VCGs), using the innovative features extracted from the geometrical and kinematic properties within VCGs. This boosts the accuracy and sensitivity of traditional MI detection.
Open Access
Retirement Annuities: Optimization, Analysis and Machine Learning
(2023-12-08) Nikolic, Branislav; Salisbury, Tom
Over the last few decades, we have seen a steady shift away from Defined Benefit (DB) pension plans to Defined Contribution (DC) pension plans in the United States. Even though a deferred income annuity (DIA) purchased while saving for retirement can pay aguaranteed stream of income for life, practically serving as a pension substitute, several questions arise. Our main contribution is answering the question of purchasing DIAs under the interest rate uncertainty. We pose the question as an optimal control problem, solve its centerpiece Hamilton-Jacobi-Bellman equation numerically, and provide a verification theorem. The result is an optimal DIA purchasing map. With Cash Refund Income Annuities (CRIA) gaining traction quickly over the past few years, the literature is growing in the area of price sensitivity and its viability when viewed through the lens of key pricing parameters, particularly insurance loading. To that end, we explored the effect of reserving requirements on pricing and have analytically proven that, if accounted for properly at the beginning, reserving requirements would be satisfied at any time during the lifetime of the annuity. Lower interest rates in the last decade prompted the explosion of fixed indexed annuities (FIAs) in the United States. These popular insurance policies offered a growth component with the addition of a lifetime income provisions. In FIAs, accumulation is achieved through exposure to a variety of indices while offering principal protection guarantees. The vast array of new products and features have created the need for a means of consistent comparisons between FIA products available to consumers. We illustr ate that statistical issues in the temporal and cross-sectional return correlations of indices used in FIAs necessitates more sophisticated modelling than is currently employed. We outline few novel approaches to handle these two issues. We model the risk control mechanisms of a class of FIA indices using machine learning. This is done using a small set of core macroeconomic variables as modelling features. This makes for more robust cross-sectional comparisons. Then we outline the properties of a sufficient model for said features, namely ‘rough’ stochastic volatility.
Open Access
Adolescent Vaping Behaviors: Exploring the Dynamics of a Social Contagion Model
(2023-12-08) Machado-Marques, Sarah Isabella; Moyles, Iain
Vaping, or the use of electronic cigarettes (e-cigarettes), is an ongoing issue for public health. The rapid increase in e-cigarette usage, particularly among adolescents, has often been referred to as an epidemic. Drawing upon this epidemiological analogy between vaping and infectious diseases as a theoretical framework, we aim to study this issue through mathematical modeling to better understand the underlying dynamics. In this thesis, we present a deterministic compartmental model of adolescent e-cigarette smoking which accounts for social influences on initiation, relapse, and cessation behaviors. We use results from a sensitivity analysis of the model’s parameters on various response variables to identify key influences on system dynamics and simplify the model into one that can be analyzed more thoroughly. Through steady state and stability analyses and simulations of the model, we conclude that (1) social influences from and on temporary quitters are not important in overall model dynamics and (2) social influences from permanent quitters can have a significant impact on long-term system dynamics, including the reduction of the smokers' equilibrium and emergence of multiple smoking waves.