Financial Risk Processes: Stochastic and Statistical Models and their Applications. On the one hand, the misuse of complex financial instruments has contributed to recent major disasters in the Australian financial and insurance industries; on the other hand, great benefits can be obtained by correct use of these kinds of instruments, to share risk between markets and segments of markets. The overall research effort in Australia in these areas is relatively small. This project will target the de ....Financial Risk Processes: Stochastic and Statistical Models and their Applications. On the one hand, the misuse of complex financial instruments has contributed to recent major disasters in the Australian financial and insurance industries; on the other hand, great benefits can be obtained by correct use of these kinds of instruments, to share risk between markets and segments of markets. The overall research effort in Australia in these areas is relatively small. This project will target the development of cutting edge technologies underlying the use of financial derivatives, not presently studied in this country or elsewhere, by bringing together a variety of top level international researchers in an integrated effort to lift the Australian understanding and application of this methodology.Read moreRead less
Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This proj ....Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project will answer many fundamental questions about large, random hypergraphs. The expected outcomes of the project also include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.Read moreRead less
A new model for random discrete structures: distributions, counting and sampling. Random discrete structures are used in countless applications across science for modelling complex systems. This project will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. This project will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics a ....A new model for random discrete structures: distributions, counting and sampling. Random discrete structures are used in countless applications across science for modelling complex systems. This project will study a new, very general model of random discrete structures which encapsulates both random networks and random matrices. This project will develop general tools for working with this model, thereby unlocking the model for use by practitioners in areas such as physics, biology, statistics and cryptography. The questions that will be tackled are fundamental problems in probability, and include as special cases the analysis of subgraph distribution in models of random networks, and the joint distribution of entries of contingency tables, which are important in statistics.Read moreRead less
Stochastic analysis and the development and application of financial risk processes. Ensuring the stability of Australia's financial system requires an understanding of the complex financial instruments, strategies and technologies that have evolved in recent years. A strong well-integrated research effort in stochastic analysis with particular application to financial markets is fundamental for measuring and managing risk, to protect and preserve a well functioning system, and to inform policy ....Stochastic analysis and the development and application of financial risk processes. Ensuring the stability of Australia's financial system requires an understanding of the complex financial instruments, strategies and technologies that have evolved in recent years. A strong well-integrated research effort in stochastic analysis with particular application to financial markets is fundamental for measuring and managing risk, to protect and preserve a well functioning system, and to inform policy debate on financial strategies and insurance liabilities.
These challenges are global and require extensive international research collaboration and interaction. The present project will enhance Australia's contributions in this area and facilitate its global impact more than is possible through individual efforts.Read moreRead less
Frontiers of Risk Modelling: Dependence and Extremes of Levy Processes. This project plans to continue an ongoing theoretical study into continuous-time stochastic processes, concentrating on developing tools for the further analysis and understanding of extremal and multivariate phenomena with applications to portfolio analysis, value-at risk calculations and complex financial instruments, with particular emphasis on practical applications of the methodologies in the insurance and finance indus ....Frontiers of Risk Modelling: Dependence and Extremes of Levy Processes. This project plans to continue an ongoing theoretical study into continuous-time stochastic processes, concentrating on developing tools for the further analysis and understanding of extremal and multivariate phenomena with applications to portfolio analysis, value-at risk calculations and complex financial instruments, with particular emphasis on practical applications of the methodologies in the insurance and finance industries. Expected outcomes would be of direct interest to these industries as well as having significant mathematical interest.Read moreRead less
Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, ....Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, with an emphasis on modern tools in Empirical Processes Theory and the theory of Random Matrices.Read moreRead less
The Mathematical and Philosophical Foundations of Probability. We find probability wherever we find uncertainty: virtually everywhere in our lives. Probability is essential to almost every technology. High-stakes decisions are routinely made on the basis of probability judgments and risk assessment-for example, in engineering, medicine, agriculture, environmental management, urban planning, public policy, public health, the law, and in our national defence. And some of those decisions have been ....The Mathematical and Philosophical Foundations of Probability. We find probability wherever we find uncertainty: virtually everywhere in our lives. Probability is essential to almost every technology. High-stakes decisions are routinely made on the basis of probability judgments and risk assessment-for example, in engineering, medicine, agriculture, environmental management, urban planning, public policy, public health, the law, and in our national defence. And some of those decisions have been made badly because of poor probability estimates-witness the 1986 space shuttle disaster. Our current methodologies for using probability are inadequate. This project will make an important contribution to the collective enterprise of enhancing our understanding of probability and its myriad applications.Read moreRead less
Stochastic Analysis with a View to Applications in Financial Risk Processes. Recent decades have seen explosive growth in applications of probability theory and statistics to the modelling of risk in finance and insurance. An intensive theoretical investigation into passage time and other problems for Levy and other continuous time processes will be applied to financial risk analyses. Related investigations will involve perpetuities and stochastic volatility models for price series. Outcomes ....Stochastic Analysis with a View to Applications in Financial Risk Processes. Recent decades have seen explosive growth in applications of probability theory and statistics to the modelling of risk in finance and insurance. An intensive theoretical investigation into passage time and other problems for Levy and other continuous time processes will be applied to financial risk analyses. Related investigations will involve perpetuities and stochastic volatility models for price series. Outcomes will include the development of new theory in probability and statistics, the initiation and reinforcement of collaborative ties with major international research figures, and the fostering of contacts with the finance industry.Read moreRead less