Risk and Reliability in Stochastic Optimisation and Equilibrium. This project seeks to develop theory and methodology in optimisation which take advantage of recent progress in understanding and treating risk in decision making. Problems of optimisation in the face of uncertainty must confront the risk inherent in having to make reliable decisions before knowing the outcomes of crucial random variables on which costs and constraints may depend. Recent theoretical developments, featuring ‘measure ....Risk and Reliability in Stochastic Optimisation and Equilibrium. This project seeks to develop theory and methodology in optimisation which take advantage of recent progress in understanding and treating risk in decision making. Problems of optimisation in the face of uncertainty must confront the risk inherent in having to make reliable decisions before knowing the outcomes of crucial random variables on which costs and constraints may depend. Recent theoretical developments, featuring ‘measures of risk’ beyond just-expected values and quantiles offer hope of major new advances. This project aims to achieve such advances not only in optimisation but also in models of equilibrium that likewise have to deal with uncertainty. Extending current theory and methodology to such multi-stage stochastic models is a challenge. Besides taking up this challenge for its own sake, a major goal of this research will be to use the results in solution algorithms.Read moreRead less
Improving risk management based on short-term stochastic forecast for financial decisions. The project targets the problems of strategy selection in the framework of mathematical finance. The aim is to find ways to reduce the impact of forecast errors in the presence of uncertainty. Related forecasting algorithms and solutions of optimization problems will be obtained.
Corporate governance, corporate disclosure policies and the timeliness of price discovery: How competitive is the Australian equity market? This project will help reduce the economic cost of poor corporate governance. It will facilitate more liquid financial markets and potentially it will increase the number and value of worthwhile investment opportunities by lowering the cost to finance them. It will assess Australia's competitive standing in the world's equity markets and establish whether ou ....Corporate governance, corporate disclosure policies and the timeliness of price discovery: How competitive is the Australian equity market? This project will help reduce the economic cost of poor corporate governance. It will facilitate more liquid financial markets and potentially it will increase the number and value of worthwhile investment opportunities by lowering the cost to finance them. It will assess Australia's competitive standing in the world's equity markets and establish whether our market is indeed transparent and a good place to raise risk capital. It will add needed credibility to corporate governance regulation. And it will enhance Australia's standing in the international research community because its research methods can be applied to almost any public capital market.Read moreRead less
Entropic Analysis of Financial Risk and Uncertainty. The recent financial crisis has shown that the financial markets are not as stable as expected, and are at risk from a lack of knowledge about new financial products and their risks. This research provides a framework to better measure and forecast financial risks by applying a set of techniques known collectively as entropic analysis as a novel way to measure the amount of information that can be extracted from historical data. The research w ....Entropic Analysis of Financial Risk and Uncertainty. The recent financial crisis has shown that the financial markets are not as stable as expected, and are at risk from a lack of knowledge about new financial products and their risks. This research provides a framework to better measure and forecast financial risks by applying a set of techniques known collectively as entropic analysis as a novel way to measure the amount of information that can be extracted from historical data. The research will facilitate the design of policies and regulations by regulatory authorities that need to evaluate new financial products, their associated risks and their impacts on the financial markets.Read moreRead less
Modelling a portfolio of financial assets: structure, estimation, testing and forecasting. Information regarding financial returns and risk is essential for optimal portfolio selection and asset management. Returns and risk have typically been analysed for individual assets. The project provides a theoretical solution to the important practical problem of modelling a portfolio of financial assets in realistic situations. The significance of the research is the development of a new approach to an ....Modelling a portfolio of financial assets: structure, estimation, testing and forecasting. Information regarding financial returns and risk is essential for optimal portfolio selection and asset management. Returns and risk have typically been analysed for individual assets. The project provides a theoretical solution to the important practical problem of modelling a portfolio of financial assets in realistic situations. The significance of the research is the development of a new approach to analyse a portfolio of returns and risk, and the determination of its applicability using numerical simulation techniques. The expected outcomes are an optimal practical method for analysing a portfolio of assets, a scientific monograph, and publications in leading international journals.Read moreRead less
Symmetrical graphs, generalized polygons and expanders. This project proposes to study a class of highly symmetrical graphs -- locally s-arc-transitive graphs. Studying the class of graphs has been one of the central topics in algebraic graph theory for over 50 years. This class of graphs has been effectively used in computer science, communication network, group theory, geometry, and other areas. This project will develop new methods to solve several fundamental problems regarding locally s-arc ....Symmetrical graphs, generalized polygons and expanders. This project proposes to study a class of highly symmetrical graphs -- locally s-arc-transitive graphs. Studying the class of graphs has been one of the central topics in algebraic graph theory for over 50 years. This class of graphs has been effectively used in computer science, communication network, group theory, geometry, and other areas. This project will develop new methods to solve several fundamental problems regarding locally s-arc-transitive graphs, and apply the outcomes to solve important problems in communication networks, graph theory, group theory, and geometry.Read moreRead less
Numerical Algorithms for Constructing Feedback Control Laws. Many decision making problems in engineering, finance and management are governed by optimal feedback control systems. These systems are normally too complex to be solved by conventional numerical methods. In this project, we propose to develop novel numerical algorithms for constructing feedback control laws. We will also investigate the procatical significance of these algorithms for solving real-world problems. The outcome of the pr ....Numerical Algorithms for Constructing Feedback Control Laws. Many decision making problems in engineering, finance and management are governed by optimal feedback control systems. These systems are normally too complex to be solved by conventional numerical methods. In this project, we propose to develop novel numerical algorithms for constructing feedback control laws. We will also investigate the procatical significance of these algorithms for solving real-world problems. The outcome of the project will provide efficient and accurate tools for constructing feedback laws in high dimensions.Read moreRead less
Exact structure in graphs and matroids. One of the main goals of mathematics is to understand and describe the structure of the mathematical world. This project will contribute to this goal, and deepen our understanding of the fundamental mathematical structures called graphs and matroids, by providing exact structural descriptions of a number of important minor-closed classes.
Real chromatic roots of graphs and matroids. This project will develop the theory of real chromatic roots of graphs, especially as it applies to minor-closed classes of graphs, with the aim of extending this theory to minor-closed classes of matroids. One of the fundamental results from the study of real chromatic roots in graph theory is that any minor-closed class of graphs has an absolute upper bound on its chromatic roots. However, while many results on minor-closed classes on graphs have cl ....Real chromatic roots of graphs and matroids. This project will develop the theory of real chromatic roots of graphs, especially as it applies to minor-closed classes of graphs, with the aim of extending this theory to minor-closed classes of matroids. One of the fundamental results from the study of real chromatic roots in graph theory is that any minor-closed class of graphs has an absolute upper bound on its chromatic roots. However, while many results on minor-closed classes on graphs have close analogues or mild variants for minor-closed classes of matroids, this upper bound on real chromatic roots appears, somewhat mysteriously, to apply only to graphs. By studying the upper root-free intervals of minor-closed classes of matroids, this project aims to shed light on this phenomenon.Read moreRead less
Symmetries of finite digraphs. Highly symmetrical graphs are well-studied and, in many respects, the theory for dealing with them is well-established. By comparison, our understanding of symmetrical digraphs is much poorer. There are some rather basic questions about these about which we know shamefully little. The aim of this project is to remedy this shortage of knowledge by extending many important results and theories about symmetrical graphs to digraphs.