◆ Portfolio selection and stochastic control
Stochastic control studies general optimization problems in a stochastic environment. As an important application, portfolio selection provides an investment framework by maximizing the expected return for a given level of risk. To capture stylized characteristics of financial assets and investors’ behaviors, we have been working on market making, stochastic volatility modeling, model uncertainty, and time-inconsistency.
◆ Financial econometrics
There has been an increasing need to use statistical methods and economic theory to examine quantitative problems in finance, which include volatility modelling, risk assessment, derivative pricing, portfolio allocation, hedging analysis, among others. This research area involves an integration of finance, economics, statistics, and applied mathematics. It aims to develop theoretical techniques and methods for various problems in finance, perform estimation for important quantities, conduct analysis of economic and financial outcomes, and provide guidance for forecasting.
◆ Behavioural Finance
Conventional finance theory relies on the theory of rational decision-making. Investors are assumed to be rational and risk averse. The seminal work of Kahneman & Tversky (1979) – “Prospect Theory: An Analysis of Decision under Risk” – reveals that decision makers are inconsistent with their risk preferences in different situations. Since then, more and more researchers strive to study investment decisions beyond rationality. Behavioural finance is the field that studies how investors make actual financial decisions. It offers a great insight in explaining many financial phenomena in the real world such as asset price bubbles, herd behaviour and heterogeneous expectations in the financial market.
◆ Computational Mathematics
As an important branch of mathematics, computational mathematics has several directions, one of which focuses on numerical methods for partial differential equations (PDEs). Numerical PDEs are widely studied and applied in academia and industrial. Most physical PDEs cannot be solved analytically, proper numerical methods are designed, in the consideration of accuracy and convergence, so that the numerical approximation to the true solution can be obtained on the discrete grid.