Newsletter No. 161

2 No. 161 19th March 2000 CUHK Newsletter CHINA HOPE PROJECT PER SONNEL RECEIVE TRAINING ON CU CAMPUS T he University's Department of Social Work is offering an intensive professional training course to senior executives of the China Hope Project from March to April. The first of its kind for social work personnel from mainland China, the course is jointly organized with the China Youth Development Foundation and is sponsored by The Asia Foundation. There w i l l be lectures, agency v i s i t s, and f i e l d placements, through which senior administrators of the China Hope Project may acquire knowledge and skills in welfare service management and the administration of charitable organizations. The China Youth Development Foundation is a very important youth and welfare organization on the mainland which aims at solving the problem of poverty and p r ov i d i ng nine-year universal education for children. One of its projects, the China Hope Project, has since 1989 built over 7,000 primary schools on the mainland and helped more than two million school-aged children resume their studies. Officiating at the opening ceremony of the training course, which took place on 26th February, were Prof. Kenneth Young, pro-vice-chancellor of The Chinese University (left 1), Dr. Allen Choate, programme development director of The Asia Foundation (right 1), Mr. Tu Meng, deputy secretary-general of the China Youth Development Foundation (left 2), and Prof. Joyce Ma, chairman of the Department of Social Work (right 2). Teaching Cell on Web-Based Teaching T wenty-two participants joined the Teaching Cell session organized by the Teaching Development Unit and facilitated by Prof. Kevin Au of the Department of International Business on 18th February 2000. The theme was 'Strategic Challenge of Web-Based Teaching: Analysing Education as an Information Business'. RESEARCH FOCUS Decisions, Decisions, Decisions! New Challenges in the Optimization of Stochastic Diffusion Processes Decisions Under Uncertainty Consider the following: 1. An investor has $ 1,000,000 which can be invested in a savings bank account offering a fixed annual interest rate of 20 per cent. How much should she put in the account in order to maximize the return? 2. A man gives away $10 to anyone walking past him in the street. How many passers-by should he give the money to in order to minimize his total loss? You may find both questions trivial or even silly. They are, in fact, concerned with deterministic systems, systems which contain no element of uncertainty, hence their answers can be accurately predicted, or, as in this case, are self- evident. However, not all practical problems are completely predictable, like the above. Now i f the questions are rewritten as follows: 1. An investor has $1,000,000 to be invested in a stock that has a past annual return of 20 per cent. How much should she put in the stock in order to maximize the expected return? 2. A casino owner gives away $10 to everyone entering his casino. How many persons should he give the money to in order to maximize the potential profit? These revised questions immediately become meaningful and do not have easy solutions. They now belong to stochastic systems which, as opposed to deterministic systems, contain an element of uncertainty or randomness in the relationship between input and direct effect. It is this inherent uncertainty that makes the questions meaningful. Although the stock in question 1 has had an annual return of 20 per cent, the possibility that it may go wrong prevents a wise investor from putting all her money on it. The second situation is just the opposite. While it is possible that all the gamblers will leave after gambling away the $10, the casino owner is willing to take the chance that some will end up losing more. Such is life — full of risks and uncertainty. However, in the first situation, the uncertainty is to the disadvantage of the investor, whereas in the second, it is to the advantage of the casino owner. How should the investor and the casino owner decide? In the jargon of systems engineering and engineering management, the second set of problems are stochastic optimization problems, following the so-called diffusion model. Of various stochastic optimization problems, the diffusion model has received particular attention from researchers, because its examples abound in life and it has wide application. For example, a stock's price can be modelled as a diffusion process, as it is the combined result of many independent buying and selling forces. The range of applications of the diffusion model includes queuing and inventory systems, and a variety of physical, biological, economic, and management systems. It has especially important applications in finance, such as in portfolio optimization, risk hedging, the consumption model, inflation control, and asset pricing. Because of this, stochastic optimization problems have been studied for years and the stochastic dynamic optimization theory for making optimal decisions was established as a result of such studies. Widely believed to be sound and inclusive, the theory was, however, problematized by certain interesting and surprising observations made recently by Prof. Zhou Xunyu of the University's Department of Systems Engineering and Engineering Management and his colleagues, observations which led to a research project supported by the Hong Kong Research Grants Council. Is Control the Larger the Better? To find an optimal answer to the two sensible questions above, one would need more information in order to quantify and evaluate the uncertainty or risk involved. The aim of Prof. Zhou's research is to do just that using a model called Linear-Quadratic (LQ) Optimal Control, a dynamic optimization model commonly used by researchers to calculate how to make optimal decisions in deterministic as well as stochastic systems. Ac co r d i ng to the model, the decision-maker applies a dynamic decision with the aim of achieving a certain goal. In mathematical terms, the goal is measured by the square (hence 'quadratic' ) ofthe difference between the current state and the ideal state of the system, while the cost incurred in applying the control is measured by square of the control. A decision-maker has to strike a balance between the performance of the control and its cost in order to get overall best results. In the LQ literature, it has been a