Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions ....Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions and estimate the errors involved. Applications include analysis of data in insurance, finance, flood prediction in hydrology.Read moreRead less
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
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
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
A Principled Approach to Computer Simulation of Dynamic General Equilibrium Macroeconomic Models. In the last two decades a new generation of computer-intensive
modeling techniques has risen to prominence in macroeconomics. These
methods have broad policy applications, from public finance and
reserve bank operation to analysis of long-run productivity growth,
taxation reform, unemployment, international trade policy and natural
resource conservation. The size and complexity of these model ....A Principled Approach to Computer Simulation of Dynamic General Equilibrium Macroeconomic Models. In the last two decades a new generation of computer-intensive
modeling techniques has risen to prominence in macroeconomics. These
methods have broad policy applications, from public finance and
reserve bank operation to analysis of long-run productivity growth,
taxation reform, unemployment, international trade policy and natural
resource conservation. The size and complexity of these models means
that even computer-based techniques will rely for the foreseeable
future on efficient program design to solve them. The project will
construct a comprehensive set of solution techniques and software for
this class of macroeconomic models, including detailed mathematical
analysis on accuracy of model output.Read moreRead less
Aggregating Generalised Stochastic Petri Nets for improved Performance Analysis. Australia's economy is very dependent on the operation of complex man-made systems. Important examples are telecommunication networks and services (e.g. the Internet), manufacturing plants, organisational processes, military logistics and transport systems (e.g. air traffic control). The performance of these systems is critical to their success. Thus being able to predict performance before systems are implemented i ....Aggregating Generalised Stochastic Petri Nets for improved Performance Analysis. Australia's economy is very dependent on the operation of complex man-made systems. Important examples are telecommunication networks and services (e.g. the Internet), manufacturing plants, organisational processes, military logistics and transport systems (e.g. air traffic control). The performance of these systems is critical to their success. Thus being able to predict performance before systems are implemented is very important in their design. This project will develop leading-edge performance analysis techniques and tools for an important class of practical systems. There is potential to commercialise the resulting tools and methodology and to transfer the expertise to industry.Read moreRead less
Optimal Control of Stochastic Partial Differential Equations. The problem to control a stochastic process so as to minimize a certain cost functional arises in many areas of Applied Sciences, Engineering and Mathematical Finance. An important practical question is to find, for a given cost functional, the optimizing control in a feedback form. We propose new tools to construct such optimal controls for a class of stochastic processes which are solutions to stochastic partial differential equati ....Optimal Control of Stochastic Partial Differential Equations. The problem to control a stochastic process so as to minimize a certain cost functional arises in many areas of Applied Sciences, Engineering and Mathematical Finance. An important practical question is to find, for a given cost functional, the optimizing control in a feedback form. We propose new tools to construct such optimal controls for a class of stochastic processes which are solutions to stochastic partial differential equations. As an outcome of this project we will obtain methods to determine the optimal control policies for a large variety of cost functionals and degenerated stochastic partial differential equations, in particular those arising in modelling of volatility in Finance.Read moreRead less
The estimation of genotype-phenotype relationships from family data and of animal abundance from capture-recapture data with frequent capture occasions: A semiparametric approach. Semiparametric statistical methods allow researchers to only model those features of their data that are of interest, but still allow standard statistical inferences to be made about these features. The aim here is to develop non standard applications of semiparametric statistical methods in the estimation of genotype ....The estimation of genotype-phenotype relationships from family data and of animal abundance from capture-recapture data with frequent capture occasions: A semiparametric approach. Semiparametric statistical methods allow researchers to only model those features of their data that are of interest, but still allow standard statistical inferences to be made about these features. The aim here is to develop non standard applications of semiparametric statistical methods in the estimation of genotype-phenotype relationships from family data and the estimation of animal abundance from capture-recapture data. The methods will be applied to real data and their theoretical properties developed. The practical significance of the project is the flexible new statistical methods that will become available to researchers. The theoretical significance will be the insights into semiparametric methods gained by developing these nonstandard applications. The expected outcomes are the new statistical procedures and the resulting theoretical insights into semiparametric statistics.Read moreRead less
Investment Approaches and Applications in Financial Markets: Evolutionary Kernel Based Subset Time-Series Using Semi-Parametric Approaches. The project will develop new investment assessments based on subset time-series modeling. Innovative evolutionary kernel smoothing algorithms using semi-parametric approaches will be introduced. The project will make three important applications of this modeling in financial markets: a) benchmarking and evaluation of inflation-indexed bonds; b) evaluation of ....Investment Approaches and Applications in Financial Markets: Evolutionary Kernel Based Subset Time-Series Using Semi-Parametric Approaches. The project will develop new investment assessments based on subset time-series modeling. Innovative evolutionary kernel smoothing algorithms using semi-parametric approaches will be introduced. The project will make three important applications of this modeling in financial markets: a) benchmarking and evaluation of inflation-indexed bonds; b) evaluation of the performance of global diversified investment funds; and c) prediction to provide early warning of the emergence of destabilising deflation or inflation. These three applications will lead to improved risk management practices and investment performance. Recursive algorithms will provide new statistical methods to study investment asset price movements and market volatility.
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The improvement of climate change investigations by developing and applying innovative evolutionary subset time series modelling using semi-parametric sparse-patterned approaches. With an estimated US$6.98 trillion loss indicated in the Stern review, severe climate change will make world climate conditions harsher and more likely include large natural climate disasters. The health of the Australian economy is critically dependent on decisions of environmental managers. However, most problems of ....The improvement of climate change investigations by developing and applying innovative evolutionary subset time series modelling using semi-parametric sparse-patterned approaches. With an estimated US$6.98 trillion loss indicated in the Stern review, severe climate change will make world climate conditions harsher and more likely include large natural climate disasters. The health of the Australian economy is critically dependent on decisions of environmental managers. However, most problems of complexity arising in climate change involve issues on which we do not possess a deep understanding. This project draws upon a set of inter-disciplinary concepts and models centred in neural networks that enable us to advance our understanding of complexity, leading to superior quantitative tools and models to allow for improved environmental decision-making.
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