Financial Engineering

The stability of financial markets benefits billions of people.  In order to respond to the challenge of maintaining healthy and stable markets, today’s systems engineers must possess quantitative and business know-how to understand and manage the complexity of financial instruments and inter-bank dynamics.
Systems engineers master the core skills of modelling economic and human behaviours, and provide insights regarding how to reach economic, social and individual investors’ objectives.

Financial engineering covers modelling, analysis, implementation of financial decision making and risk management.  More than just theories, systems engineers develop practical tools with a combination of multiple disciplines including statistics, probability, optimization and stochastic analysis.  Related research topics include pricing and hedging, systematic risk management, stochastic volatility models, and portfolio choice.
 

Behavioural Portfolio Selection
X.Y. Zhou
We study portfolio selection models where the classical utility function is replaced by behavioural criteria featuring S-shaped value function and probability distortion. Implications on capital asset pricing will be investigated.

High Frequency Trading
N. Chen
High frequency trading (HFT) is to use computers to process market information and make elaborate decisions to "initiate buy/sell orders.  As of July 2009, HFT firms account for 73% of all US equity trading volumes."  We study how to develop realistic and analytically tractable models for the dynamics of order-driven trading systems.  The implications on optimal execution and investment strategies will be investigated.

Index Tracking with Stochastic Linear Quadratic Controls Using Semidefinite Programming
D.D. Yao, S. Zhang and X.Y. Zhou
We solve stochastic linear quadratic control problems using a newly developed technique known as semidefinite programming.  We further develop a software system through which a simple portfolio tracking a financial index, such as the stock index or a steady growth rate, can be formed using this technique.

Knowledge-based Chaotic Prediction for Financial Engineering Applications
K.P. Lam
Financial time series, such as stock prices, options and indices, are often highly erratic and contain complex behaviours which make their accurate prediction, even on a short-term basis, extremely difficult. Recently, Barahona and Poon’s work (1996) on deterministic chaos detection has generated much interest in short-term prediction of nonlinear time series.  Empirical study under a wide range of problem context accumulates a substantial amount of ad-hoc knowledge for its effective use.  The proposed work is to extend the previous work of the principal investigator on a fuzzy expert system for technical analysis of stocks, by integrating knowledge based techniques with chaotic detection of financial time series.  The field of using chaotic prediction in finance is still not fully developed, and there is much ground for further research and development in this novel integrated scheme.  The effectiveness of the scheme would be evaluated with methodologies such as neural predictors and evolutionary computing.

Mining Streams of Financial Data and News
J. Yu
Financial market trends prediction is a technique to forecast market trend changes, which assists financial market participants to spot arbitrage opportunities for investment.  Currently, most existing reported data mining studies for trend prediction focused on the time-series perspectives.  However, there are numerous social factors that contribute to financial market trends prediction, but cannot be obtained from or represented in time-series data.  First, in order to effectively predict market trends, one main objective of this project is to develop new data mining techniques that deal with two different types of data, namely financial data (time-series data or simply data) and news articles (textual data or simply text) concurrently.  Second, stock market traders need to monitor tens of thousands of data/text sources coming as open-ended data/text streams in an on-line fashion, and need to analyse and make decisions based on the data/text streams they have received as soon as they can.  We will study trend predictions by investigating the above two interrelated issues and finding associations among multiple data/text streams.

Revised Dynamic Mean-Variance Portfolio Selection
D. Li
As the dynamic mean-variance portfolio selection formulation does not satisfy the principle of optimality of dynamic programming, phenomena of time inconsistency occur, i.e., investors may behave irrationally under the pre-committed optimal mean-variance portfolio policy when their wealth is above certain threshold during the investment process. By relaxing the self-financing restriction to allow withdrawal of money out of the market, we develop in this research a revised mean-variance policy which dominates the pre-committed optimal mean-variance portfolio policy in the sense that, while the two achieve the same mean-variance pair of the terminal wealth, the revised policy enables the investor to receive a free cash flow stream during the investment process.  This research will further carry out study on minimum-cost mean-variance portfolio selection, as the monotonicity does not hold in the mean-variance world, i.e., not the larger amount you invest, the larger expected future wealth you can expect for a given risk (variance) level.

Spectral Methods for Optimal Decision and First Passage Problems
Lingfei Li
We develop a new method based on spectral analysis to solve optimal decision problems including optimal stopping, optimal switching and stochastic games, and first passage problems for a rich class of Markov diffusions, jump-diffusions and pure jump processes, which are building blocks for empirically realistic financial models.  These problems arise in a variety of applications in financial engineering, including evaluating financial contracts with early exercise rights or/and with barriers, such as American-style options, barrier options, callable and puttable bonds and convertible bonds, and real options arising in commodity extraction, power generation, optimal investment or divestment timing, and other irreversible decisions.

Time Consistency Issue in Financial Optimization
D. Li
Choosing an appropriate risk measure for specific investor(s) is one of the most important steps in carrying out risk management in investment.  When a mean-risk measure does not possess time-consistency in efficiency, following the optimal policy derived from such a mean-risk measure may yield some irrational investment behaviours.  Unfortunately, almost all widely adopted risk measures in the literature are not time consistent, or even not time-consistent in efficiency.  Furthermore, the theoretical frameworks proposed recently in the literature on time consistency are difficult to satisfy and these abstract measures are not intuitively understandable by investors.  The objective of this research is to develop a framework to identify suitable mean-risk measures which possess desirable properties, especially, time consistency in efficiency, and, at the same time, can be intuitively understood and appreciated by investors.