The modern financial industry, comprising the banking and investment sectors, as well as insurance companies and pension funds, relies heavily on modern risk analysis and risk management. As the array of financial products grows in variety and complexity, accurate and reliable risk management has become both more complex and more essential. Several tragic failures in recent years - such as the rapid demise of Confederation Life, Enron, Barings Bank, and Long Term Capital and the subprime crisis - have highlighted the importance of sound risk management and the prudent solvency and capital requirement. These are precisely the areas where some of our faculty members have made significant contributions. Some examples include developing a framework for modelling and analyzing the risks involved in long-term insurance contracts with embedded financial guarantees such as segregated funds and variable annuities; analyzing the impact of regulation changes on the overall insurance market and how such changes affect both market stability and the risk-sharing among policyholders, insurers, and re-insurers (such as on the optimal design of insurance contracts and reinsurance arrangements under the Conditional Tail Expectation or Value at Risk objective/constraint); the behaviour of optimal credit portfolios in the "large portfolio" regime that serves as the foundation for current credit risk regulations; fast algorithms for portfolio optimization using the Omega performance measure. Another key area of research is the mortality modelling and longevity risk management, as triggered by people have been living longer than they were expected to, and this has resulted in huge financial losses in annuity and pension portfolios. We have developed stochastic mortality model, proposed sustainable hybrid pension scheme solutions that combine the best features of the defined benefit and defined contribution systems, analyzed the demographic and financial risks associated with reverse mortgage contracts, as well as devised an economic pricing model for mortality-linked securities.
The field of applied probability is quite a general one, predominantly focusing on applications of probability theory to stochastic systems arising in scientific and engineering domains including actuarial science, operations research, computer science, and finance. One of the main branches of applied probability is queuing theory, which is broadly defined as the mathematical study of waiting lines and congestion. Queuing theory finds important uses in applications as diverse as health care and computer systems performance evaluation, and it often provides the essential framework for how to efficiently streamline processes and remove/reduce bottlenecks. As more and more emphasis is being placed on the quality of service experienced by customers, there is a growing need for mathematical queuing models to incorporate realistic features such as flexible and/or preferential service policies in combination with varying job types. In today's world, queuing theorists, or more generally applied probabilists, seek to employ cutting-edge mathematical techniques in conjunction with more powerful and sophisticated computational resources to help them analyze, in a tractable way, more complicated stochastic processes which, in turn, more precisely reflect real-world conditions.
Biostatistics is an exciting area of statistics devoted to the development and application of innovative methods for using data to answer important questions in areas ranging from clinical trials, population health to biological science. When evaluating new pharmaceutical treatments biostatisticians play an important role in all phases of drug development through the design and analysis of clinical trials. In population health research biostatisticians can work closely with epidemiologists in the design of cross-sectional, cohort or retrospective studies to elucidate the causal mechanisms of chronic disease. In biology interest may lie in how individual organisms or ecosystems respond to pollutants through the analysis of experimental or observational data. Our department has a strong record of impact in a diverse range of areas in biostatistics. Our strengths include the analysis of life history data, longitudinal data analysis, the design and analysis of clinical trials, epidemiological studies, clustered data, methods for dealing with incomplete data and measurement error, causal inference and studies of biological systems.
Business and Industrial Statistics develops and applies quantitative methods and paradigms for inquiry and decision-making in business and industrial contexts. In business and industry, a wide variety of data is routinely collected from customers, products and processes. Using statistics-based quality and process improvement methods, such as Six Sigma or Statistical Engineering, we combine these existing data streams together with additional data from planned studies. The goal is to increase productivity, reduce costs, make better decisions and have more satisfied customers. Our department has research strengths in experimental design, control charting, observational studies, problem-solving systems and measurement system assessment. We have business contacts through the Business and Industrial Statistics Research Group (BISRG).
Ongoing and seemingly relentless technological advances have made computers an indispensable tool for the modern statistician. One hand, "big data" are becoming commonplace in areas of research such as brain imaging, high-frequency trading, machine learning, quality control, and climatology. Not only are sophisticated computational techniques required to be efficiently scalable to these large datasets, but their high dimensionality also calls for innovative methods of visualization, dimension reduction, and data-mining. On the other hand, the new technology encourages the use of more complex and realistic statistical models, prohibitively intractable only a decade ago. Such models may incorporate missing data imputation mechanisms, random effects, or intricate patterns of spatial and temporal dependence. Inference, prediction, and extreme value analysis for these models is an active area of departmental research, leading to the development of many algorithms and software packages involving Monte Carlo and quasi Monte Carlo methods, approximation by surrogate models, and a variety of problem-specific optimization techniques.
The pricing and the hedging of assets, the management of investment portfolios and risks of many kinds, are problems which require both underlying statistical models together with computational methods for assessing these models and drawing conclusions from them. Many traditional models fail to capture the more extreme behaviour of markets, behaviour which has the greatest impact on the economy and investment decisions. For this reason, more appropriate but complex models are often adopted which frequently require numerical or Monte Carlo methods for inference. These research areas include topics in financial time series and econometrics, option pricing, and computational and Monte Carlo models and methods for hedging, portfolio management and assessing risk.
The modelling and analysis of the claims experience on a portfolio of business and how it unfolds over time are longstanding and important actuarial research problems. Incorporation of the incidence and severity of claims necessitates the use of a variety of quantitative tools from applied probability and related areas of stochastic jump processes. Recent mathematical advances, coupled with the ready availability of computational resources, allows for the use of more complex and realistic insurance claim models. Sound financial risk management is thus enhanced by the use of these approaches. Our department continues to provide research leadership internationally in the area of insurance risk theory and loss models. In particular, our strengths are in analysis of surplus, analysis of insurance loss and other statistical distributions with particular emphasis on right tail behaviour, stochastic ordering and dependence among risks, and applications to reinsurance and claims reserving.
Statistical models are key to understanding the natural, experimental and technological processes in the world around us. They are ubiquitous and arise in diverse fields including economics, finance and actuarial science, manufacturing, pattern recognition, shape analysis, and the study of chronic disease. Modern datasets are typically massive, often obtained from complex sampling designs, and are subject to other complexities such as incomplete information. They require highly sophisticated methods and algorithms for their statistical analysis to reveal important relationships, facilitate causal inferences, and make predictions. All decision-making or other inference in the presence of uncertainty implicitly requires statistical models of the extent and nature of this uncertainty. Statistical modeling and Inference are thus not only at the foundation of the statistical sciences, but at the core of all inference drawn from data. Since the inception of our department, faculty members have made pioneering contributions to the important field of statistical inference, having made key advances in the theory and applications of likelihood and estimating functions methodology.
Scientific surveys of human and natural populations typically have complex probability sampling designs. Constructing sampling designs which are economical and efficient for inference is an important part of survey methodology. Once the data have been collected, analyses of the data must take into account both the complex sampling procedures and sources of non-sampling error such as non-response, missing data and measurement error. Besides extending the repertoire of techniques available for analyses, a survey methodologist has opportunities to work with researchers in other disciplines and sectors on the design of sampling and modern data collection methods for specific surveys. Our faculty include several specialists in survey methods, who are pursuing both theoretical and applied research. Topics include the analysis of longitudinal and survival data from complex surveys, the use of empirical likelihood in survey analysis, and the treatment of samples collected from several frames and with multiple data collection modes. The Survey Research Centre, a joint venture with the Department of Sociology and Legal Studies, provides advice and carries out survey fieldwork for researchers in all faculties of the University.
