Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and ....Two-price quantitative finance. This project aims to establish a novel field, namely two-price quantitative finance, and explore its applications. The new field will integrate two major schools for modelling and explain the presence of two prices, the buying and selling prices, widely observed in the real-world markets, and the equilibrium approach from the fundamental law of one price. The outcomes would deepen our understanding of the fundamental relationship among liquidity, prices, risk and the economy. This project expects to bring about long-term impact on quantitative finance and related applications through providing a deep understanding of, and a new perspective for, the design, risk and fairness of the finance, property and insurance markets.Read moreRead less
G-expectation and its applications to nonlinear risk management. This project will develop novel theories and methods for nonlinear risk management based on nonlinear expectations and Backward Stochastic Differential Equations. The expected outcomes of the project will place Australia in the forefront and the leading position of these fields.
Discovery Early Career Researcher Award - Grant ID: DE120102388
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
From Bayesian filtering to smoothing and prediction for multiple object systems. This project will develop new and improved algorithms for tracking multiple targets, such as tanks, submarines or planes, using the state of the art in mathematical and computational design. These will enable more efficient and accurate technologies for defence related applications including intelligence, surveillance and reconnaissance.
Parameter estimation for multi-object systems. Parameter estimation in multi-object system is essential to the application of multi-object filtering to a wider range of practical problems with social and commercial benefits. This project develops the necessary parameter estimation techniques for complete 'plug-and-play' multi-object filtering solutions that facilitates widespread applications.
The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to ....The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to be singular. This project aims to reveal the underlying mathematical structures and develop new computational algorithms to analyse a general class of perturbed systems both locally near an isolated singularity and globally. It plans to use these algorithms to solve systems of equations, calculate generalised inverse operators, examine perturbed Markov processes, and estimate exit times from meta-stable states in stochastic population dynamics.Read moreRead less
A stochastic geometric framework for Bayesian sensor array processing. This project develops a mathematical framework, and a new generation of techniques, for sensor array processing to address real-world problems with uncertainty in array parameters and number of signals. The outcomes will enhance the capability of sensors in many application areas including, radar, sonar, astronomy and wireless communications.
Estimation and Control of Noisy Riemannian Systems. Many application areas such as satellite control, computer vision, coordination of rigid bodies, require the estimation and control of systems subject to geometric constraints. Most current algorithms for doing this are deterministic and can fail catastrophically in the presence of noise. This project aims to provide:
(i) Methods for analysing and then redesigning deterministic algorithms to ensure stability in the presence of noise;
(ii) New ....Estimation and Control of Noisy Riemannian Systems. Many application areas such as satellite control, computer vision, coordination of rigid bodies, require the estimation and control of systems subject to geometric constraints. Most current algorithms for doing this are deterministic and can fail catastrophically in the presence of noise. This project aims to provide:
(i) Methods for analysing and then redesigning deterministic algorithms to ensure stability in the presence of noise;
(ii) New design methods that deal with noise in an optimal way;
(iii) Noise resistant methods for distributed consensus seeking systems and cooperative control systems.
The outcomes will advance and benefit spatio-temporal data analysis and coordination in areas such as transport, health and video-security.Read moreRead less
Point processes system identification under simultaneity. Neuroscientists study neuronal brain dynamics of mammals via recordings from scores of tiny electrodes. But analysing these experiments is a problem because current methods cannot handle the common case where neurons discharge simultaneously. This project aims to provide powerful new tools to overcome this bottleneck.
Riemannian System Identification. A growing number of applications such as satellite attitude estimation, pose estimation in computer vision and direction estimation in statistics require the study of random processes in Riemannian manifolds and Lie Groups. This project will provide: methods for the construction/ numerical simulation of such processes; methods of system identification and their asymptotic performance analysis; and, algorithms for process state estimation.
Modeling stochastic systems in Riemannian manifolds. This project aims to develop new statistical signal processing and control engineering algorithms and tools that will enable tracking of objects remotely on land and in space. A growing number of applications require the study of random processes in Riemannian manifolds, that is processes that evolve subject to a geometric constraint. This project aims to provide methods for the numerical simulation of such processes, methods of online and off ....Modeling stochastic systems in Riemannian manifolds. This project aims to develop new statistical signal processing and control engineering algorithms and tools that will enable tracking of objects remotely on land and in space. A growing number of applications require the study of random processes in Riemannian manifolds, that is processes that evolve subject to a geometric constraint. This project aims to provide methods for the numerical simulation of such processes, methods of online and offline system identification from data on such processes and asymptotic performance analysis; and algorithms for process state estimation that obeys the geometry. The outcomes will advance and benefit spatio-temporal data analysis in areas such as transport, health and video-security.Read moreRead less