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by Ki-sing Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaves 30.

by Lo Yiu Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 89-90). / Abstract also in Chinese. / Abstract --- p.iii / Acknowledgements --- p.iv / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Main Idea --- p.5 / Chapter 1.2. --- Organization --- p.8 / Chapter Chapter 2. --- Geometric and Analytic Preliminaries --- p.9 / Chapter 2.1. --- A Review on Measure Theory --- p.9 / Chapter 2.2. --- Submanifolds in Rn --- p.11 / Chapter 2.3. --- Several Results from PDEs --- p.17 / Chapter 2.4. --- Biharmonic Comparison Lemma --- p.20 / Chapter Chapter 3. --- Approximate Graphical Decomposition --- p.24 / Chapter 3.1. --- Some Preliminaries --- p.24 / Chapter 3.2. --- Approximate Graphical Decomposition --- p.30 / Chapter Chapter 4. --- Existence & Regularity of Measure-theoretic Limits of Minimizing Sequence --- p.41 / Chapter 4.1. --- Willmore Functional and Area --- p.41 / Chapter 4.2. --- Existence of Measure-theoretic Limit of Minimizing Sequence --- p.45 / Chapter 4.3. --- Higher Regularity at Good Points --- p.54 / Chapter 4.4. --- Convergence in Hausdorff Distance Sense --- p.62 / Chapter 4.5. --- Regularity near Bad Points --- p.64 / Chapter Chapter 5. --- Existence of Genus 1 Minimizers in Rn --- p.83 / References --- p.89

No description available.

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by Chun Gu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 69-71). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.3 / Chapter 2 --- Definitions --- p.7 / Chapter 3 --- Some Previous Work on OBDD --- p.13 / Chapter 3.1 --- The Work of Bryant --- p.13 / Chapter 3.2 --- Some Variations of the OBDD --- p.14 / Chapter 3.3 --- Previous Work on Variable Ordering of OBDD --- p.16 / Chapter 3.3.1 --- The FIH Heuristic --- p.16 / Chapter 3.3.2 --- The Dynamic Variable Ordering --- p.17 / Chapter 3.3.3 --- The Interleaving method --- p.19 / Chapter 4 --- Two Level Logic Function and OBDD --- p.21 / Chapter 5 --- DSCF Algorithm --- p.25 / Chapter 6 --- Thin Boolean Function --- p.33 / Chapter 6.1 --- The Structure and Properties of thin Boolean functions --- p.33 / Chapter 6.1.1 --- The construction of Thin OBDDs --- p.33 / Chapter 6.1.2 --- Properties of Thin Boolean Functions --- p.38 / Chapter 6.1.3 --- Thin Factored Functions --- p.49 / Chapter 6.2 --- The Revised DSCF Algorithm --- p.52 / Chapter 6.3 --- Experimental Results --- p.54 / Chapter 7 --- A Pattern Merging Algorithm --- p.59 / Chapter 7.1 --- Merging of Patterns --- p.60 / Chapter 7.2 --- The Algorithm --- p.62 / Chapter 7.3 --- Experiments and Conclusion --- p.65 / Chapter 8 --- Conclusions --- p.67

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.

Li, Rui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 69-71). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Portfolio Selection Models --- p.1 / Chapter 1.1.1 --- Single Period Models --- p.2 / Chapter 1.1.2 --- Multi-Period Models --- p.4 / Chapter 1.1.3 --- Continuous-Time Model --- p.5 / Chapter 1.2 --- Description and Motivation of New Model --- p.6 / Chapter 1.3 --- Major Contributions --- p.7 / Chapter 1.4 --- Thesis Organization --- p.8 / Chapter 2 --- Formulation and General Methodology --- p.9 / Chapter 2.1 --- Formulation --- p.9 / Chapter 2.1.1 --- Dynamics --- p.10 / Chapter 2.1.2 --- General Form --- p.13 / Chapter 2.1.3 --- Assumptions --- p.13 / Chapter 2.2 --- Methodology --- p.15 / Chapter 2.2.1 --- Weighting Problem --- p.15 / Chapter 2.2.2 --- Search For Optimal Weighting Coefficient --- p.19 / Chapter 3 --- Model I: A Trade-off Between Risk and Return Is Given --- p.22 / Chapter 3.1 --- Problem Formulation --- p.22 / Chapter 3.2 --- Solution to the Parameterized Weighting Problem (PWP(γ)) --- p.23 / Chapter 3.2.1 --- "Construction of the Auxiliary Problem A(γ, λ)" --- p.24 / Chapter 3.2.2 --- Discussion on Parameter A --- p.29 / Chapter 3.3 --- Algorithm --- p.39 / Chapter 4 --- Model II: Expected Return Level Is Specified --- p.42 / Chapter 4.1 --- Problem Formulation --- p.42 / Chapter 4.2 --- Optimal Max-Min Solution --- p.44 / Chapter 4.3 --- Discussion on Parameter λ --- p.50 / Chapter 4.4 --- Algorithm --- p.55 / Chapter 5 --- Numerical Examples --- p.58 / Chapter 6 --- Conclusions --- p.67 / Bibliography --- p.71

Wong, Chi Ying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 71-74). / Abstracts in English and Chinese. / Abstract Page --- p.ii / Acknowledgment Page --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.5 / Chapter 3 --- Review of minimax portfolio selection model --- p.11 / Chapter 3.1 --- The I∞ model --- p.11 / Chapter 4 --- Portfolio optimization with group investment limits --- p.16 / Chapter 4.1 --- The model --- p.16 / Chapter 4.2 --- The optimal investment strategy --- p.17 / Chapter 4.2.1 --- All assets are risky --- p.18 / Chapter 4.2.2 --- Some riskfree assets are involved --- p.39 / Chapter 4.3 --- Chapter summary --- p.40 / Chapter 5 --- Tracing out the efficient frontier --- p.41 / Chapter 5.1 --- Properties of the efficient frontier --- p.42 / Chapter 5.2 --- The algorithm --- p.51 / Chapter 5.3 --- Time complexity of the algorithm --- p.56 / Chapter 5.4 --- Chapter summary --- p.57 / Chapter 6 --- Finding the investor's optimal portfolio --- p.58 / Chapter 6.1 --- Investor's portfolio with given A --- p.58 / Chapter 6.2 --- Chapter summary --- p.60 / Chapter 7 --- Numerical experiments --- p.61 / Chapter 7.1 --- Finding the efficient frontier numerically --- p.61 / Chapter 7.2 --- Performance between mean-variance model and I∞ model --- p.64 / Chapter 7.2.1 --- Data analysis --- p.64 / Chapter 7.2.2 --- Experiment description and discussion --- p.65 / Chapter 7.3 --- Chapter summary --- p.67 / Chapter 8 --- Conclusion --- p.68 / Bibliography --- p.71 / Appendix --- p.75 / Chapter A --- Stocks for finding the efficient frontiers with and without bound constraints --- p.75 / Chapter B --- List of companies --- p.77 / Chapter C --- Graphical Results --- p.81

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy