Li Yan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 87-88). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.8 / Chapter 2.1 --- Markowitz´ةs Single-Period Mean-Variance Model --- p.9 / Chapter 2.2 --- Discrete-Time Mean-Variance Problem --- p.10 / Chapter 2.2.1 --- Optimal Buy-and-Hold Policy --- p.11 / Chapter 2.2.2 --- Optimal Rolling Markowitz Policy --- p.12 / Chapter 2.2.3 --- Multi-Period Mean-Variance Optimal Policy --- p.12 / Chapter 2.3 --- Continuous-Time Market --- p.13 / Chapter 2.3.1 --- Optimal Unconstrained Policy --- p.15 / Chapter 2.3.2 --- Bankruptcy Prohibited Optimal Policy --- p.16 / Chapter 2.3.3 --- No-Shorting Optimal Policy --- p.17 / Chapter 2.4 --- Continuously Rebalancing Optimal Policy --- p.18 / Chapter 3 --- Discretized Continuous-Time Optimal Policies --- p.20 / Chapter 3.1 --- Problem Setup --- p.21 / Chapter 3.2 --- Unconstrained Problem --- p.25 / Chapter 3.3 --- Problem with No-shorting Constraint --- p.31 / Chapter 3.4 --- Problem with No-Bankruptcy Constraint --- p.34 / Chapter 3.4.1 --- Quasi No-Bankruptcy Problem --- p.36 / Chapter 3.5 --- Stability of the Simulation --- p.38 / Chapter 3.6 --- Concluding Remarks --- p.41 / Chapter 4 --- Performance of Continuous-Time M-V Optimal Policies --- p.43 / Chapter 4.1 --- Measures of the Performance by Probabilities --- p.45 / Chapter 4.2 --- Performance of the Optimal Mean-Variance Portfolio --- p.51 / Chapter 4.2.1 --- Target-Hitting Probability --- p.51 / Chapter 4.2.2 --- Cut-Off Probability --- p.53 / Chapter 4.2.3 --- Target-Hitting-before-Cut-Off Probability --- p.58 / Chapter 4.3 --- Numerical Evaluations of Probabilities for Discrete-Time Market --- p.63 / Chapter 4.3.1 --- Simulation on Target-Hitting Probability --- p.64 / Chapter 4.3.2 --- Simulation on Zero-Hitting Probability --- p.66 / Chapter 4.3.3 --- Simulation on Target-Hitting-before-Bankruptcy Probability --- p.67 / Chapter 4.4 --- Policy Comparison --- p.68 / Chapter 4.4.1 --- Profile of the Probabilities --- p.70 / Chapter 4.4.2 --- Impact of z on the Probabilities --- p.72 / Chapter 4.5 --- Concluding Remarks --- p.74 / Chapter 5 --- Empirical Analysis --- p.75 / Chapter 5.1 --- Experiment Description and Parameter Estimation --- p.76 / Chapter 5.1.1 --- Introduction of the Data --- p.76 / Chapter 5.1.2 --- Experiment Description --- p.77 / Chapter 5.1.3 --- Parameter Estimation --- p.79 / Chapter 5.2 --- Empirical Results and Analysis --- p.80 / Chapter 5.2.1 --- Performance Indicator --- p.80 / Chapter 5.2.2 --- Experimental Results and Analysis --- p.81 / Chapter 5.3 --- Concluding Remarks --- p.83 / Chapter 6 --- Summary --- p.84 / Bibliography --- p.87

Hou, Wenting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 113-117). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Literature Review --- p.1 / Chapter 1.2 --- Problem Description --- p.8 / Chapter 1.3 --- The Main Contributions of This Thesis --- p.11 / Chapter 2 --- Model I --- p.13 / Chapter 2.1 --- Notation --- p.13 / Chapter 2.2 --- Model Formulation --- p.16 / Chapter 2.3 --- Analytical Solution --- p.19 / Chapter 3 --- Model II --- p.25 / Chapter 3.1 --- Model Formulation --- p.25 / Chapter 3.2 --- Analytical Solution --- p.30 / Chapter 3.3 --- How to Find y --- p.38 / Chapter 3.4 --- Numerical Example --- p.42 / Chapter 4 --- Model III --- p.47 / Chapter 4.1 --- Model Formulation --- p.48 / Chapter 4.2 --- Dynamic Programming --- p.50 / Chapter 4.2.1 --- DP I --- p.50 / Chapter 4.2.2 --- DP II --- p.53 / Chapter 4.3 --- Approximate Analytical Solution --- p.56 / Chapter 4.4 --- Computational Result Comparison --- p.65 / Chapter 5 --- Conclusions --- p.73 / Chapter A --- Source Data --- p.76 / Chapter A.l --- rti --- p.76 / Chapter A.2 --- qti --- p.79 / Chapter B --- Model II Numerical Example and Result --- p.82 / Chapter B. --- l Value of xti when A = 0.3 --- p.82 / Chapter B.2 --- Value of xti when A = 0.6 --- p.84 / Chapter B.3 --- Value of xti when A = 0.9 --- p.88 / Chapter B.4 --- True Value of xti --- p.91 / Chapter C --- Model III Numerical Example and Result --- p.98 / Chapter C.l --- The Value of Mt of DP II --- p.98 / Chapter C.2 --- Track of Optimal Value of DP II --- p.101 / Chapter C.3 --- The Optimal Total Wealth of DP II --- p.105 / Chapter C.4 --- The Optimal Asset Allocation of P4 --- p.109 / Bibliography --- p.113

Dai, Juan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 36-39). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Previous Work --- p.3 / Chapter 1.2 --- Proposed Framework --- p.5 / Chapter 1.3 --- Overview --- p.6 / Chapter 2 --- Placement of the Local Classifiers --- p.8 / Chapter 2.1 --- The Uncertainty Map --- p.9 / Chapter 2.2 --- Responsibility Mixture Model --- p.11 / Chapter 2.3 --- EM for Parameter Estimation --- p.12 / Chapter 2.3.1 --- E-Step --- p.14 / Chapter 2.3.2 --- M-Step --- p.15 / Chapter 2.3.3 --- Relationship with Gaussian Mixture Mod- els(GMM) --- p.16 / Chapter 3 --- Fusing of Locally Adaptive Classifiers --- p.18 / Chapter 3.1 --- Training --- p.18 / Chapter 3.2 --- Testing --- p.21 / Chapter 4 --- Algorithmic Characteristics --- p.23 / Chapter 4.1 --- Uncertainty Piloted Placement of Local Classifiers --- p.23 / Chapter 4.2 --- Uncertainty Piloted Fusing of Local Classifiers --- p.24 / Chapter 4.3 --- Related Work --- p.25 / Chapter 5 --- Experiments --- p.27 / Chapter 5.1 --- Dimensionality Reduction --- p.27 / Chapter 5.2 --- Two-Class Classification Problem: Gender Classification --- p.29 / Chapter 5.3 --- Multi-Class Classification: Face Recognition --- p.30 / Chapter 5.3.1 --- Varying the Lighting --- p.31 / Chapter 5.3.2 --- Varying the Pose --- p.32 / Chapter 5.3.3 --- Number of Features Extracted --- p.33 / Chapter 6 --- Conclusion --- p.34 / Bibliography --- p.36

In this thesis, two problems of time consistent mean-variance portfolio selection have been studied: mean-variance asset-liability management with regime switchings and mean-variance optimization with state-dependent risk aversion under short-selling prohibition. Due to the non-linear expectation term in the mean-variance utility, the usual Tower Property fails to hold, and the corresponding optimal portfolio selection problem becomes time-inconsistent in the sense that it does not admit the Bellman Optimality Principle. Because of this, in this thesis, time-consistent equilibrium solution of two mean-variance optimization problems is established via a game theoretic approach. In the first part of this thesis, the time consistent solution of the mean-variance asset-liability management is sought for. By using the extended Hamilton-Jacobi- Bellman equation for equilibrium solution, equilibrium feedback control of this MVALM and the corresponding equilibrium value function can be obtained. The equilibrium control is found to be affine in liability. Hence, the time consistent equilibrium control of this problem is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the simple classical mean-variance problem in Björk and Murgoci (2010), in which it was independent of the state. In the second part of this thesis, the time consistent equilibrium strategies for the mean-variance portfolio selection with state dependent risk aversion under short-selling prohibition is studied in both a discrete and a continuous time set- tings. The motivation that urges us to study this problem is the recent work in Björk et al. (2012) that considered the mean-variance problem with state dependent risk aversion in the sense that the risk aversion is inversely proportional to the current wealth. There is no short-selling restriction in their problem and the corresponding time consistent control was shown to be linear in wealth. However, we discovered that the counterpart of their continuous time equilibrium control in the discrete time framework behaves unsatisfactory, in the sense that the corresponding “optimal” wealth process can take negative values. This negativity in wealth will change the investor into a risk seeker which results in an unbounded value function that is economically unsound. Therefore, the discretized version of the problem in Bjork et al. (2012) might yield solutions with bankruptcy possibility. Furthermore, such “bankruptcy” solution can converge to the solution in continuous counterpart as Björk et al. (2012). This means that the negative risk aversion drawback could appear in implementing the solution in Björk et al. (2012) discretely in practice. This drawback urges us to prohibit short-selling in order to eliminate the chance of getting non-positive wealth. Using backward induction, the equilibrium control in discrete time setting is explicit solvable and is shown to be linear in wealth. An application of the extended Hamilton-Jacobi-Bellman equation leads us to conclude that the continuous time equilibrium control is also linear in wealth. Also, the investment to wealth ratio would satisfy an integral equation which is uniquely solvable. The discrete time equilibrium controls are shown to converge to that in continuous time setting. / published_or_final_version / Mathematics / Master / Master of Philosophy

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Man Po Kong = 信貸相聯票據和住宅按揭的預期損失之估值 / 文普綱. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 85-86). / Text in English; abstracts in English and Chinese. / Man Po Kong = Xin dai xiang lian piao ju he zhu zhai an jie de yu qi sun shi zhi gu zhi / Wen Pugang. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Structural model --- p.3 / Chapter 2.1 --- Merton's model --- p.3 / Chapter 2.2 --- The term structure of interest rate --- p.7 / Chapter 2.3 --- The default-triggering mechanism and derivations from strict priority rule --- p.9 / Chapter 2.4 --- Stationary leverage ratio --- p.11 / Chapter 2.5 --- The three-factor structural model --- p.12 / Chapter 3 --- Credit-linked Notes with early default risk --- p.18 / Chapter 3.1 --- Introduction to credit-linked notes --- p.18 / Chapter 3.2 --- The pricing of credit-linked notes --- p.20 / Chapter 3.3 --- Non mean-reverting leverage ratios --- p.21 / Chapter 3.3.1 --- Special case (pQv=0) --- p.23 / Chapter 3.4 --- Mean reverting leverage ratios --- p.25 / Chapter 4 --- Numerical results and discussion --- p.28 / Chapter 4.1 --- Exact solution (KQ=kv=PQv=PVr=0) --- p.31 / Chapter 4.2 --- "Lower bound approximation (kQ,kv≠0,pQr,pvr≠0)" --- p.37 / Chapter 4.2.1 --- Effect of interest rate --- p.43 / Chapter 4.3 --- Monte Carlo simulation (PQV≠0) --- p.47 / Chapter 5 --- Expected loss of residential mortgage loans --- p.56 / Chapter 5.1 --- Introduction to residential mortgage loans --- p.56 / Chapter 5.2 --- Calculation of expected loss of residential mortgage loans --- p.59 / Chapter 6 --- Numerical results and discussion --- p.65 / Chapter 6.1 --- Numerical results --- p.65 / Chapter 7 --- Conclusion --- p.73 / Chapter A --- Methodology --- p.75 / Chapter A.1 --- Monte Carlo Simulation --- p.76 / Chapter A.2 --- Finding lower and upper bound approach --- p.79 / Chapter A.2.1 --- Single stage approximation --- p.79 / Chapter A.2.2 --- Multistage lower bound approximation --- p.82 / Bibliography --- p.85

Yeung Kin Bong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 69-73). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Credit risk modeling --- p.3 / Chapter 1.2 --- Uniqueness of bi-directional: hybrid system --- p.4 / Chapter 1.3 --- Scope of the study --- p.5 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- Statistical / Empirical approach --- p.6 / Chapter 2.2 --- Structural approach --- p.8 / Chapter 3 --- Background --- p.10 / Chapter 3.1 --- Merton structural default model --- p.10 / Chapter 3.2 --- Cross-sectional regression analysis (CRA) --- p.15 / Chapter 3.3 --- Neural network learning (NN) --- p.16 / Chapter 3.3.1 --- Single-layer network --- p.17 / Chapter 3.3.2 --- Multi-layer perceptron (MLP) --- p.20 / Chapter 3.3.3 --- Back-propagation network --- p.22 / Chapter 3.3.4 --- "Supervised, unsupervised and combine unsupervised-supervised learning" --- p.23 / Chapter 3.4 --- Weaknesses of uni-directional modeling --- p.23 / Chapter 4 --- Methodology --- p.26 / Chapter 4.1 --- Bi-directional modeling --- p.26 / Chapter 4.2 --- Asset price estimation --- p.31 / Chapter 4.3 --- Quantifying accounting data noise --- p.33 / Chapter 5 --- Proposed Model --- p.37 / Chapter 5.1 --- Core of the model --- p.37 / Chapter 5.2 --- Feature selection --- p.41 / Chapter 5.3 --- Bi-directional default neural system --- p.44 / Chapter 6 --- Implementations --- p.49 / Chapter 6.1 --- Data preparation --- p.50 / Chapter 6.2 --- Experiment --- p.51 / Chapter 6.3 --- Empirical results --- p.61 / Chapter 6.3.1 --- Predicted spreads from the uni-directional models --- p.61 / Chapter 6.3.2 --- Predicted spreads from the proposed bi-directional model --- p.63 / Chapter 6.3.3 --- Performance comparison --- p.64 / Chapter 7 --- Conclusions --- p.67 / Bibliography --- p.69

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.