Qing Liu. Quantifying COVID-19: Modeling and Evaluation, PhD thesis, Feb 2022, UTS

The coronavirus disease 2019 (COVID-19) has evolved to a global pandemic and poses significant demands and challenges in modeling its complex epidemic transmission, infection, and contagion. Moreover, it has shown to be vastly different
from known epidemics. To address the COVID-19 pandemic, significant efforts have been made to model COVID-19 transmission, diagnoses, interventions, and pathological and influence analysis, etc. However, due to the unique and unknown problem and data complexity, the related studies of COVID-19 still face numerous challenges, including undocumented infections, asymptomatic contagion, uncertainty and quality issues in the reported data, flexible external non-pharmaceutical interventions, unknown resurgence patterns or periodicity, and multiple mutations.

This thesis aims to understand COVID-19 concerning the COVID-19 research landscape, transmission complexity, non-pharmaceutical interventions, and COVID-19 resurgence. Focusing on the COVID-19 challenges, this thesis first compares the key characteristics of COVID-19 disease with several known epidemics, and it summarizes the COVID-19 modeling complexities caused by these attributes. Starting from this basic knowledge, this thesis further explores COVID-19 modeling, which results in the following four contributions. (1) This thesis tracks the current COVID-19 modeling progress with natural language techniques and statistically summarizes the major facts of COVID- 19 disease and COVID-19 modelling. This work structures a transdisciplinary research landscape and provides a holistic picture of COVID-19 modeling. (2) It infers the possible quantity of undocumented infections in the early stage of the COVID-19 outbreak with the proposed density-based Bayesian probabilistic compartmental model. This work examines the COVID-19 transmission complexities, in other words, undocumented infections, contagion reinforcement, and the imperfect conditions existing in COVID-19 reported data, that is, noise, sparsity, and uncertainty. (3)With the proposed event-driven generalized Susceptible-Exposed-Infectious-Recovered compartmental model, this thesis studies the impact of external interventions and activities in the dynamic COVID-19 evolving process and quantifies the efficacy of control policies and relaxation measures. (4) This thesis compares the differences between multiple COVID-19 waves, including the epidemiological attributes and the countermeasures, and it simulates the possible scenarios with different interventions and virus mutations. This exploration illustrates the possible reasons for COVID-19 resurgence and provides reliable guidance for society resuscitation.

Extensive experiments, including mean-field Bayesian inference, backward-looking empirical evaluations, forward-looking simulations, and short-term forecast, demonstrate the effectiveness of the proposed methods for modeling the COVID-19 complexities aforementioned. The findings and quantitative results in this thesis indicate clues, evidence, and guidance for governments and policymakers to appropriately manage and mitigate the COVID-19 pandemic.

Jia Xu. High-dimensional Dependence Modelling for Cross-market Analysis, PhD thesis, Feb 2022, UTS

In the age of the information explosion, data mining and machine learning techniques have become heavily involved in financial market modelling. Many scholars have demonstrated the significance of dependence modelling across the multiple financial markets, especially during the catastrophic global financial crisis (GFC) in 2008. Sharp fluctuations across different markets demonstrate that the dependence is high-dimensional, contains various hierarchical and horizontal relationships, and often presents complicated dependence structures and characteristics such as an asymmetrical structure and tail dependence. Thus, a strong understanding of cross-market dependence is critical in cross-market applications such as portfolio management and risk management.

Unfortunately, modelling the dependence across multiple financial markets is highly challenging for the following reasons: (i) the cross-market dependence structure is often embedded with strong and complicated coupling relationships of high dimensionality as with any complex behavioural and social system; (ii) financial variables such as daily return have been demonstrated to follow non-Gaussian distributions, which means that dependence models should cover a wide range of dependencies to capture the asymmetric dependencies; and (iii) various tail dependencies such as lower and upper tail dependence are ubiquitous in financial markets.

Typical approaches such as Markov models, probabilistic graphical models, and neural network models could have advantages by building a conditional dependence structure between random variables to resolve the high dimensional problem. However, these models always impose unrealistic assumptions (e.g., Gaussian or mixtures of it), which leads to failure in capturing the complex dependence structures in the real world. In addition, copulas have been demonstrated to be effective in presenting dependence between variables in the statistics and finance communities. By splitting the joint distribution into dependence between variables and independent marginal distributions, copulas provide a flexible mechanism for investigating the specifications of the dependence across the market and the marginal distributions independently. Nevertheless, building effective dependence structures to address the aforementioned complexities is still a significant challenge for existing copula approaches. Over the last decade, various mixed models (e.g., tree-structured copula models and copula Bayesian networks) have been developed by utilising the advantages of both traditional copula models and probabilistic graphical models; however, assumptions and restrictions on the dependence structure have still not been avoided.

Based on the aforementioned research limitations and challenges, this thesis proposes weighted partial D vine copula, weighted partial regular vine copula and weighted regular vine variational long short-term memory (LSTM) models for high-dimensional cross-market modelling.

In Chapter 4, a novel bottom-to-top approach with no prior dependence assumptions called a weighted partial D vine copula is presented to capture the nonlinear and asymmetric dependence structures of cross-market data. By releasing these restrictions regarding the Gaussian assumptions, the new model is able to capture more sophisticated dependence structures between variables. The new modelling outcomes are applied to stock and exchange markets data as a case study, the extensive experimental results demonstrate that this model and its intrinsic design significantly outperform typical models and industry baselines.

Chapter 5 extends the approach presented in Chapter 4 to a more general structure, namely weighted partial regular vine. The new model can capture the nonlinear and asymmetric dependence structures with more flexible way by utilising the advantages of the regular vine structure and non-restricted bivariate copula families. Then, the application of model for asset allocation by optimising the utility of a portfolio is presented as a case study. Compared with the general approaches, such as minimum variance, the optimised utility function using the new weighted partial regular vine can avoid the Gaussian assumption, which is always implied in these models due to computational issues.

Chapter 6 discusses the benefits of taking flexible bivariate copulas with different tail dependencies using the new regular vine copula model. Experiments are conducted to implement the new model on the exchange market to analyse the dynamic movement of the tail dependencies, consequently demonstrating better performance.

Chapter 7 introduces a novel vine copula-based variational autoencoder (VAE) to generate randomness for LSTM to model the cross-market data. Current VAE models usually apply mean-field assumption to simplify the calculation process; however, such an assumption may lead to posterior collapse by removing the dependencies between variables. Our new model provides a two-step parameter estimation process to be incorporated with variational LSTM for capturing the complex dependencies on latent variables. By maintaining such dependency relationships over latent variables, the empirical results demonstrate a dramatic improvement for cross-market data modelling and avoid posterior collapse.

All of the aforementioned approaches and frameworks for high-dimensional cross-market dependence modelling are applied in accordance with business applications, such as value at risk. These models not only provide insightful knowledge for investors to control and reduce the aggregation risk of the portfolio, but also show promising potential for further exploration and development.