Duy-Minh Dang

Machine Learning for Defined Contribution Superannuation

In a landscape of economic uncertainty and rising inflation, managing retirement savings and wealth has become a pressing challenge in finance. This complexity is amplified by a significant global shift towards Defined Contribution (DC) superannuation plans, particularly prominent in Australia. Under DC plans, individuals shoulder the entire investment risk through both the accumulation (pre-retirement) and decumulation (post-retirement) phases, which together constitute a full-life cycle DC plan extending over potentially 50 years or more.

With Australia being the world's fourth-largest holder of pension fund assets and with over 87% of its 2.77 trillion USD superannuation assets in DC plans, a vast majority of Australian employees and retirees face considerable risk in retirement. Alarmingly, the fear of outliving retirement savings often surpasses the fear of death among many pre-retirees.

Given this background, we offer a range of projects designed to harness the power of machine learning in modelling and managing Defined Contribution superannuation through a stochastic control approach. These projects aim to:

• Identify and quantify the diverse risk factors in DC plans, providing insights for suitable risk measures for effective wealth management.
• Develop robust, efficient, and reliable investment strategies for both the pre- and post-retirement phases through a stochastic control framework
• Deliver personalised, effective wealth management solutions that cater to individual needs, thus alleviating the fear of outlivig retirement savings.
• Promote a quantitative understanding of retirement savings among Australian employees and retirees, particularly emphasisng the challenges faced during the decumulation phase.

These projects, suitable for Honours, Master and PhD level students, present students with the opportunity to work at the forefront of financial mathematics, leveraging machine learning methods to enhance the competitiveness of Australian super funds. These endeavors aim to drive significant economic and societal benefits, particularly relevant to Australia, while offering students the chance to make a real-world impact in addressing one of the most challenging issues in today's society.

Numerical Methods for Hamilton-Jacobi-Bellman Equations in Finance

Many popular problems in financial mathematics can be posed in terms of a stochastic optimal control formulation, leading to the formulation of nonlinear Hamilton-Jacobi-Bellman (HJB) equations. The inherent challenges in solving these HJB equations include the lack of analytical solutions under realistic scenarios where controls are constrained, and the non-uniqueness and lack of smooth classical solutions due to their nonlinear nature. Consequently, our pursuit is directed towards finding the financially relevant solution for these HJB equations – the viscosity solution in this context.

A number of my projects are centered around the development of efficient numerical methods that ensure convergence to the viscosity solution for HJB equations arising in finance. Potential applications include portfolio optimisation (superannuation), variable annuities with riders (pension products), and valuation adjustments (regulations).

These projects, suitable for Honours, Master and PhD level students, emphasize the practical and real-world relevance of research in mathematical finance, offering opportunities for intellectual growth and for making meaningful contributions to understanding and controlling complex financial systems.