For economists who study the growth theories, the most critical issues they are trying to deal with are the sources of long-term growth and the problem of inequality. Stimulated by the endogenous growth theories, a substantial amount of studies focus on how technology improvement and human capital in education promote economic growth. In this thesis, however, we focus on another important source of growth, the role of health in generating economic growth and generating development traps. We discuss the issues of long-term growth and inequality in the first two essays respectively and examine empirically the relationship between health and economic growth in the last essay. / In the first essay, we analyze the endogenous growth generated by health accumulation. We extend the Barro (1996b) model to consider both the positive and negative effects of health by endogenizing the health depreciation rate. We consider three forms of health depreciation rate: constant health depreciation rate, health depreciation rate determined only by health, and health depreciation rate determined simultaneously by health and education. We also consider the situation when health affects economic growth through entering the utility function directly. By comparing the results from the optimization processes, we find that whether health enters the utility function does not affect long-term growth. What really matters is the specific form of health depreciation rate. / In the last essay, we complement the first two essays by analyzing empirically the relationship between health expenditure and economic growth. We summarize that there are three main categories of macroeconomic empirical research on the relationship between health and economic growth. Relatively few focuses on how health investment affects economic growth. We analyze this relationship in the last essay by employing both the Mankiw, Romer and Weil (1992) model and the Bassanini and Scarpetta (2001) model. Several econometric methods are used for robustness checking. The statistical results show that health expenditure at least has non-negative effect on economic growth. / In the second essay, we analyze the issue of health related development traps. Various mechanisms of health related development traps have been proposed by recent literature. The general characteristics of these mechanisms are that there are stable multiple equilibriums. However, the statistics show that the gap between the rich countries and the poor ones are actually widening from 1960 to 2007. To explain this phenomenon, we develop another mechanism to generate health related development traps, through which the gap between the developed and developing countries is widening. To check the sensitivity of the results to the specific form of health utility function, we also employ a more general form of health utility function. / Huang, Liang. / Adviser: Li Hongyi. / Source: Dissertation Abstracts International, Volume: 72-04, Section: A, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 201-218). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The classical mean-variance model treats the upside and downside equally as risks. This feature is undesirable, in the eyes of a profit-making investor. In this regard, the downside Lower Partial Moments (LPM) are more attractive as alternative risk measures, since they only penalize the downside. This thesis is mainly concerned with the issues related to downside risk measures. We consider two different environments, under which our investigations shall proceed. The first one is the world of Q-radial distributions. The Q-radial distributions generalize the normal distribution and uniform distribution, among many other useful classes of probability distributions. The second type of setting that we will investigate assumes that the distribution of the assets' returns is ambiguous, and the only available (and reliable) knowledge that we have is the first few moments of the distribution. In the first setting, we show that if the investment return rates follow a Q-radial distribution, then the LPM related Risk Adjusted Performance Measures (RAPM), such as the Sortino ratio, the Omega Statistic, the upside potential ratio, and the normalized LPM, are all equivalent to the ordinary Sharpe ratio, which is easy to compute and optimize. Conversely, if all normalized LPM's are equivalent to the Sharpe ratio, then the underlying distribution must be Q-radial. Therefore, this property characterizes the class of Q-radial distributions in which the Sharpe ratio is essentially the only risk adjusted performance measure. If the distribution is unspecified, and only the first few moments (first, second, and/or fourth) are known, we develop tight upper bounds on the lower partial moment E[(r -- X+m], where r ∈ reals and X is stochastic. Based on such tight bounds we then consider the corresponding robust portfolio selection problem, in which the distribution of the investment return is ambiguous, but its first few moments are assumed to be known. We show that if the first two moments are known and the risk measures are either the lower partial moments or the Conditional Value-at-Risk (CVaR), then the optimal portfolio is mean-variance efficient. Moreover, one can formulate the (adjustable) two-stage robust portfolio selection problem as a convex program with finite representations. If more than two moments are known, then the problem is NP-hard in general. In that case we consider approximative models instead. We then proceed to consider the problem of how to alleviate regrets in a decision problem when the parameters are ambiguous, or part of the information will only become known in a dynamic fashion. Since the models we consider in this thesis are mostly in the minimax format, we also consider a general minimax model and study a progressive finite representation approach, which can be used to prove the minimax theorem constructively without any fixed-point theorem or hyperplane separation theorems. / Chen, Li. / Adviser: Shuzhong Zhang. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3762. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 106-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Then, we consider the patterns between news stream and time series indices stream. We first transform the news stream into a set of bursty feature (keywords) time series streams and propose three technique to study their relationship to time series index. First, we explore a Non-homogeneous Hidden Markov Model (NHMM) to predict the stock market process which takes both stock prices and news articles into consideration. Second, we propose a risk analytical model to predict the volatility of price indices by integrating news information. Finally, we devise an algorithm to detect the priming event from text and a time series index. The evaluation on real world dataset suggests the significant correlation exists between news stream and time series stream and our pattern discover algorithm can detect promising patterns from this relationship to support real world applications effectively. / We start from investigating the co-movement relationship of multiple time series. We propose techniques to study two aspects of this problem. First, we propose a co-movement model for constructing financial portfolio by analyzing and mining the co-movement patterns among two time series. Second, we presents an efficient streaming algorithm to discover leaders from multiple time series stream. Both of the algorithms are evaluated using real time series indices data and the result proves that co-movement patterns and detected leaders are promising and can support various applications including portfolio management, high frequency trading and risk management. / With the increasing amount of data in financial market, there are two types of data streams attracting a lot of research and studies, time series index stream and related news stream. In this thesis, we focus on discovering patterns from these data streams and try to answer the following challenging questions, (I) given two co-evolving time series indices, what is the co-movement dependency between them. (II) given a set of evolving time series, could we detect some leaders from them whose rise or fall impacts the behavior of many other time series? (III) could we integrate the news stream information into stock price prediction? (IV) could we integrate the news stream information into stock risk analysis? and (V) could we detect what are those events that trigger time series index movement. For each of the question, we design algorithms and address three technique issues (I) how to detect promising patterns from the noisy financial data; (II) how to update the old patterns when new data arrives in high frequency; (III) how to use the pattern to support the financial applications. / Wu, Di. / Adviser: Jeffrey Xu Pu. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 124-131). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

In Part I of the thesis, we focus on the fast and efficient algorithms for the TV-L1 minimization problem which can be applied to recover the blurred images corrupted by impulse noise. We construct the half-quadratic algorithm (HQA) for TV-L1 image restoration based on the half-quadratic technique. By introducing the proximal point algorithm into the HQA, we then obtain a modified HQA. We call it the proximal point half-quadratice algorithm (PHA). We introduce the PHA aiming to decrease the condition number of the coefficient matrix as updating the iterator in HQA. Until recently, there have been many efficient methods to solve the TV-L1 minimization problem. Examples are the primal-dual method, the fast total variational deconvolution method (FTVDM), and the augmented Lagrangian method (ALM). By numerical results of the FTVDM and ALM, we see that the images restored by these methods may sometimes appear to be blocky. Come back to our methods. The HQA and the PHA are both fast and efficient algorithms to solve the TV-L1 minimization problem. We prove that our algorithms are both majorize-minimize algorithms for solving a regularized TV-L1 problem. Given the assumption ker(∇)∩ker(BT B) = {0}, the convergence and linear convergence of the HQA is then easily obtained. Without such an assumption, a convergence result of PHA is also obtained. We apply our algorithms to deblur images corrupted with impulse noise. The results show that the HQA is faster and more accurate than the ALM and FTVDM for salt-and-pepper noise and comparable to the two methods for random-valued impulse noise. The PHA is comparable to the HQA in both recovered effect and computing consuming. Comparing with ALM and FTVDM, the PHA is faster and more accurate than ALM and FTVDM for salt-and-pepper noise and comparable to the two methods for random-valued impulse noise. Furthermore, the recovered images by the HQA and the PHA are less blocky. / In this thesis, we study two aspects in image processing. Part I is on the fast and efficient algorithms for the TV-L1 image restoration. Part II is on the fast and efficient algorithms for the positively constraint maximum penalized TV image restoration. / Part II of the thesis focuses on the positively constraint maximum penalized total variation image restoration. We develop and implement a multiplicative iteration approach for the positively constrained total variation image restoration. We call our algorithm MITV. The MITV algorithm is based on the multiplicative iterative algorithm originally developed for tomographic image reconstruction. The advantages of the MITV are that it is very easy to derive and implement under different image noise models and it respects the positivity constraint. Our method can be applied to kinds of noise models, the Gaussian noise model, Poisson noise model and the impulse noise model. In numerical test, we apply our algorithm to deblur images corrupted with Gaussian noise. The results show that our method give better restored images than the forward-backward splitting algorithm. / Liang, Haixia. / Adviser: Hon Fu Raymond Chan. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 87-92). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

In this thesis, we focus our study on the multi-period portfolio selection problems with different investment conditions. We first analyze the mean-variance multi-period portfolio selection problem with stochastic investment horizon. It is often the case that some unexpected endogenous and exogenous events may force an investor to terminate her investment and leave the market. We give the assumption that the uncertain investment horizon follows a given stochastic process. By making use of the embedding technique of Li and Ng (2000), the original nonseparable problem can be solved by solving an auxiliary problem. With the given assumption, the auxiliary problem can be translated into one with deterministic exit time and solved by dynamic programming. Furthermore, we consider the mean-variance formulation of multi-period portfolio optimization for asset-liability management with an exogenous uncertain investment horizon. Secondly, we consider the multi-period portfolio selection problem in an incomplete market with no short-selling or transaction cost constraint. We assume that the sample space is finite, and the number of possible security price vector transitions is equal to the number of securities. By introducing a family of auxiliary markets, we connect the primal problem to a set of optimization problems without no short-selling or without transaction costs constraint. In the no short-selling case, the auxiliary problem can be solved by using the martingale method of Pliska (1986), and the optimal terminal wealth of the original constrained problem can be derived. In the transaction cost case, we find that the dual problem, which is to minimize the optimal value for the set of optimization problems, is equivalent to the primal problem, when the primal problem has a solution, and we thus characterize the optimal solution accordingly. / Yi, Lan. / Adviser: Duan Li. / Source: Dissertation Abstracts International, Volume: 72-11, Section: A, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 133-139). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

In this thesis, we mainly study the portfolio selection problem with a set of index and options of stocks, based on a refined mean-variance methodology. Models in single-stage and multistage cases are studied, with a formulation using a scenario tree structure. We first investigate the pattern of the payoff of the optimal optioned portfolio. It turns out there is a rich structure with many interesting properties, including the piecewise linearity, risk-free return at some fixed scenarios, etc. We then extend the model to accommodate the features of multistage formulations. Both the mathematical programming methodology and the stochastic control methodology are applied to solve the decision model based on a scenario tree structure. Analytical formulations of the optimal portfolio together with an expression of the efficient frontier are derived. We also make an analysis of the relations between the two approaches. We further study some variations of the mean-variance formulation. These models are applied to construct a portfolio with same preferred payoff characters, such as monotonic payoff or guaranteed payoff. Finally, the tracking model is considered in this thesis. The optimal payoff and its mean-variance efficiency are analyzed. Throughout the thesis, many numerical examples with real life data are used to illustrate and validate our results. / Liang Jianfeng. / "May 2004." / Source: Dissertation Abstracts International, Volume: 66-01, Section: B, page: 0529. / Supervisors: Duan Li; Shuzhong Zhang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 120-126). / Available also through the Internet via Current research @ Chinese University of Hong Kong under title: Optioned portfolio selection models, analysis, and solution methods / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Jin Hanqing. / "July 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 133-139). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Due to the inherent complexity of the power-controlled scheduling problem, finding optimal schedules and power allocations for large-size networks will still consume extraordinary large amounts of time despite the performance of our method. We therefore propose an approximation algorithm, called the Guaranteed and Greedy Scheduling (GGS), which can find near optimal solutions within a short runtime. GGS is a polynomial time algorithm with a provable upper bound for the approximation ratio relative to the optimal solution. / For the distributed scheduling algorithm design, we focus on the CSMA (Carrier-Sense Multiple-Access) network, which is the most widely used distributed wireless network in practice. We establish a rigorous conceptual framework, upon which effective solutions to interference-safe transmissions can be constructed under the physical interference model. Specifically, we propose to use the concept of "safe carrier sensing range", which guarantees interference-safe transmissions under the physical interference model. We further propose a novel carrier-sensing mechanism, called Incremental-Power Carrier-Sensing (IPCS), which implements the safe carrier-sensing range concept in a simple way. Extensive simulation results show that IPCS can boost spatial reuse and network throughput by more than 60% relative to the conventional carrier-sensing mechanism. / This thesis studies the wireless link scheduling problem under the physical interference model. Such problem is more realistic than the widely studied wireless scheduling problem under the protocol interference model. However, it is a challenging problem because the physical interference model considers the cumulative effect of the interference powers from all the other concurrent transmitters. This thesis covers the complexity analysis and algorithm design (both centralized and distributed) for such a challenging problem. / We first give a rigorous NP-completeness proof for the power-controlled scheduling with consecutive transmission constraint under the physical interference model. We then present a centralized scheduling algorithm based on a column generation method which finds the optimal schedules and transmit powers. We further consider an integer constraint that requires the number of time slots allocated to a link to be an integer. Building upon the column generation method, we propose a branch-and-price method which can find the optimal integer solution. By simplifying the pricing problem and designing a new branching rule, we significantly improve the efficiency of both the column generation and the branch-and-price methods. For example, the average runtime is reduced by 99.86% in 18-link networks compared with the traditional column generation method. / Fu, Liqun. / Advisers: Soung Chang Liew; Jianwei Huang. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 133-144). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

After that, the cooperative transmission scheme is extended for the scenario of more than two source-destination pairs. One objective is to investigate the relationship between the diversity order and the number of source-destination pairs. This is done by considering the sum power minimization problem. A pricing game is derived to provide a distributed implementation. At Nash Equilibrium of the game, the total transmission power is minimized. Simulation results show the rapid convergence of the game and its adaptation to channel fluctuations. It also shows that the cooperative transmission scheme achieves full diversity order. / Apart from replacing a superposition code based cooperative transmission scheme by a TDM based scheme, the implementation can be simplified by introducing a partner selection scheme to the nodes. In that network, the cooperative transmission code still uses superposition code as the building block. Instead of relaying the messages from all other nodes, in this new scheme, the source nodes only relay the messages for their assigned partners. A natural question is: How can we assign the partners to the source nodes such that the total transmission power is minimized. The problem is solved in two phases. Firstly, we solve the sum power minimization problem for each pair of nodes. In some cases, this problem has closed-form solutions while for the other cases, a simple iterative algorithm can solve this problem. / Firstly, cooperative orthogonal-division channel is defined and two cooperative transmission schemes based on dirty-paper coding and superposition code are proposed and compared through simulations. Simulation Results show the significant improvement over the pure direct transmission schemes. Although one cooperative transmission scheme achieves a slightly larger rate region, the other scheme has a much simpler implementation so the remaining parts of the thesis focus on this scheme. The outage performance of this scheme is also compared with a simplified Han-Kobayashi scheme through simulations. Simulation results illustrate the significant improvement in the diversity gain of this scheme over the Han-Kobayashi scheme. / However, it is noted that the complexity of implementing superposition code, which is a building block of the cooperative transmission code, is very high when there are many users in the network. Hence, another time-division multiplex (TDM) based cooperative transmission scheme is proposed. Similar to the superposition code based scheme, there is a pricing game which can provide a distributed sum power minimization. Simulation results also show that the game has high convergence rate and it can adapt to changes of channel conditions efficiently. In addition, this cooperative transmission scheme also achieves full diversity order. / In this thesis, different codes and resource allocation algorithms for cooperative transmissions are proposed. Briefly speaking, in cooperative transmission, a number of wireless nodes form a coalition in which they exchange and cooperatively transmit messages. As a result, the order of diversity can be increased without installing additional antennas. / Next, a weighted sum rate maximization algorithm is proposed. There are two purposes of this algorithm. Firstly, this algorithm is adopted to find the Pareto-optimal points of the boundary of the achievable rate region through simulations. Secondly, this algorithm can be extended to solve the max-min fairness problem and the joint utility maximization algorithm by the proposed framework. / This thesis is ended with some future research directions. / With this information, we can assign the partners by Gabow's algorithm, which solves the maximum weighted matching problem that is mapped from the original partner selection problem. Nonetheless, it is noted that when the number of users is very large, it involves a large amount of the communication and computational cost to solve the sum power minimization problem for each pair of nodes as well as the partner selection problem. Therefore, the Grouping Algorithm is proposed to reduce the aforementioned implementation cost. Simulation results show that the optimal algorithm and the Grouping Algorithm can achieve full diversity order. Moreover, although the Grouping Algorithm is sub-optimal in general, it costs only 1dB of the sum power more than the optimal algorithm. / Ng, Cho Yiu. / Adviser: Tal M. Lok. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 152-162). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

by Wan Shan. / "June, 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.