Multifractal models in finance via the crossing tree. High level mathematical modelling is an established part of the modern finance industry, in particular the Black-Scholes option pricing formula is now an indispensable financial tool.
To remain competitive the Australian financial sector needs to keep up with developments in mathematical finance, which is only possible if the Australian academic community remains active in the field.
The work on multifractal modelling proposed here is innov ....Multifractal models in finance via the crossing tree. High level mathematical modelling is an established part of the modern finance industry, in particular the Black-Scholes option pricing formula is now an indispensable financial tool.
To remain competitive the Australian financial sector needs to keep up with developments in mathematical finance, which is only possible if the Australian academic community remains active in the field.
The work on multifractal modelling proposed here is innovative both in its theoretical aspects and its applied methodology, and will ensure that Australian research remains at the cutting edge of this highly competitive and fast moving field.Read moreRead less
Boundary Crossing Analysis for Random Processes with Applications to Risk Management. Effective management of environmental, financial and superannuation investment risks is vitally important for Australia. Results of the project will add to the theoretical foundations of risk management and provide new computational tools for specialists working in the areas of financial engineering, insurance, superannuation funds. These tools will assist in improving risk profile evaluation and developing new ....Boundary Crossing Analysis for Random Processes with Applications to Risk Management. Effective management of environmental, financial and superannuation investment risks is vitally important for Australia. Results of the project will add to the theoretical foundations of risk management and provide new computational tools for specialists working in the areas of financial engineering, insurance, superannuation funds. These tools will assist in improving risk profile evaluation and developing new statistical control charts for security monitoring of epidemics, networks intrusions and other potentially dangerous changes. The research will also give Australia a competitive advantage in the area of education related to stochastic processes, mathematical finance, control theory and their applications.Read moreRead less
Expenditure needs and drawdown of retirement savings during later life: how important are demographic factors and financial resources? Projections of expenditure patterns in retirement which allow for population heterogeneity will provide individuals with a better appreciation of their income needs and their savings requirements for a comfortable retirement. It will also enable financial institutions to develop products which better target retirees' needs over the course of retirement, and in ad ....Expenditure needs and drawdown of retirement savings during later life: how important are demographic factors and financial resources? Projections of expenditure patterns in retirement which allow for population heterogeneity will provide individuals with a better appreciation of their income needs and their savings requirements for a comfortable retirement. It will also enable financial institutions to develop products which better target retirees' needs over the course of retirement, and in addition it will enable improved assessment of aspects of Government income support policy. Specifically, understanding the complex interactions between private and public pensions, and concession card receipt upon expenditure behaviour, will enable more accurate costings of the public support of elderly families as Australia's population ages. Read moreRead less
Censored Regression Techniques for Credit Scoring. This project will apply censored regression techniques to a loans database from the industry partner, the ANZ bank. We will accurately estimate the actual time to loan repayment, rather than simply the risk of default. In a novel approach for credit scoring we will build a model using current, right-censored, rather than historic data, incorporating loans that are not yet repaid but are underway and clearly have a length of loan longer than obse ....Censored Regression Techniques for Credit Scoring. This project will apply censored regression techniques to a loans database from the industry partner, the ANZ bank. We will accurately estimate the actual time to loan repayment, rather than simply the risk of default. In a novel approach for credit scoring we will build a model using current, right-censored, rather than historic data, incorporating loans that are not yet repaid but are underway and clearly have a length of loan longer than observed. This approach has the immense advantage of being able to reflect contemporary borrowing patterns in the model, rather than relying on historic trends.
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New Stochastic Processes with Applications in Finance. This project investigates the properties and the use of two new families of models with applications in Finance, and beyond. It will contribute to the development of fundamental research in mathematics and its applications. The project will produce more realistic financial models that will benefit researchers in this field. This will in turn have a flow on effect to benefit the wider community. The project will provide for postgraduate train ....New Stochastic Processes with Applications in Finance. This project investigates the properties and the use of two new families of models with applications in Finance, and beyond. It will contribute to the development of fundamental research in mathematics and its applications. The project will produce more realistic financial models that will benefit researchers in this field. This will in turn have a flow on effect to benefit the wider community. The project will provide for postgraduate training and international scientific exchange. Overall, the project will strengthen Australia's standing at the forefront of fundamental and applied research.Read moreRead less
Modelling with stochastic differential equations. We will develop methodology for modelling and analysis of phenomena subjected to random and uncertain influences, such as behaviour of investors in the market, evolution of economy, values of stocks and ant colonies. This methodology will enable scientists to achieve more accurate description and analysis of their models and provide better understanding of these phenomena. Creating the tools for understanding such complex systems will have far re ....Modelling with stochastic differential equations. We will develop methodology for modelling and analysis of phenomena subjected to random and uncertain influences, such as behaviour of investors in the market, evolution of economy, values of stocks and ant colonies. This methodology will enable scientists to achieve more accurate description and analysis of their models and provide better understanding of these phenomena. Creating the tools for understanding such complex systems will have far reaching benefits both nationally and internationally and will allow Australia to strengthen its position in international research. The project will also provide for postgraduate training and international scientific exchange.Read moreRead less
Stochastic systems with applications to Biology and Finance. This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Sto ....Stochastic systems with applications to Biology and Finance. This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Stochastic Volatility in Finance. The answers to these questions will underpin the statistical theory for potential breakthroughs in the respective areas. This project will contribute to the theory and applications of Stochastic Processes, as well as modelling in biology and finance.Read moreRead less
Models for Australian Electricity Derivatives. Electricity derivatives, such as electricity futures and options are used to manage the risk associated with volatility in prices of electricity. This project aims to develop models for pricing electricity derivatives specifically suited for Australia. Because of the non-storable nature of electricity the standard option pricing principle of "no-arbitrage" does not apply to electricity options, such as caps and floors, but applies to options on elec ....Models for Australian Electricity Derivatives. Electricity derivatives, such as electricity futures and options are used to manage the risk associated with volatility in prices of electricity. This project aims to develop models for pricing electricity derivatives specifically suited for Australia. Because of the non-storable nature of electricity the standard option pricing principle of "no-arbitrage" does not apply to electricity options, such as caps and floors, but applies to options on electricity futures. Therefore a specific model is needed that takes into account the pricing principle of "no-arbitrage" and combines it with other factors that drive electricity prices. The novel element in this proposal is incorporation of the weather forecasts into the models for electricity options. As a result of this study appropriate models for electricity derivatives for various geographical regions in Australia will be developed.Read moreRead less
New Statistical Procedures for Analysing Dependence in Non-Gaussian Time Series Data. In the economic, finance and business spheres, statistical data is often discrete, binary, strictly positive, or characterized by an uneven distribution of values above and below the average. Prominent examples are the high frequency financial data that have become accessible with the computerization of financial markets, including the number of trades in successive time intervals, the direction of price change ....New Statistical Procedures for Analysing Dependence in Non-Gaussian Time Series Data. In the economic, finance and business spheres, statistical data is often discrete, binary, strictly positive, or characterized by an uneven distribution of values above and below the average. Prominent examples are the high frequency financial data that have become accessible with the computerization of financial markets, including the number of trades in successive time intervals, the direction of price changes, the time between trades and the return on a financial asset over short periods. This project develops a range of new statistical tools that will enable both researchers and practitioners to analyze the dynamic behaviour in such data and thereby validate and implement a range of financial models.Read moreRead less
A Bayesian State Space Methodology for Forecasting Stock Market Volatility and Associated Time-varying Risk Premia. Accurate prediction of stock market volatility is critical for effective financial risk management. Along with information on volatility embedded in historical stock market returns, the prices of options written on the underlying stocks also reflect the option market's assessment of future volatility. This project will exploit this dual data source in a completely new way, using it ....A Bayesian State Space Methodology for Forecasting Stock Market Volatility and Associated Time-varying Risk Premia. Accurate prediction of stock market volatility is critical for effective financial risk management. Along with information on volatility embedded in historical stock market returns, the prices of options written on the underlying stocks also reflect the option market's assessment of future volatility. This project will exploit this dual data source in a completely new way, using it to produce forecasts of both volatility itself and the premia factored into asset prices as a result of traders' perceptions of volatility risk. State-of-the-art statistical methods will be used to produce up-dates of the probability of extreme volatility and/or extreme risk aversion, as new market data becomes available each trading day.Read moreRead less