published_or_final_version / abstract / Industrial and Manufacturing Systems Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

Lam Fong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 67-68). / Abstracts in English and Chinese. / Chapter 1 --- Background --- p.1 / Chapter 1.1 --- Bond and Yield --- p.1 / Chapter 1.1.1 --- Bond [8] --- p.1 / Chapter 1.1.2 --- Yields --- p.3 / Chapter 1.1.3 --- Qualitative Nature of Price-Yield Curves --- p.5 / Chapter 1.2 --- "Duration, Convexity and Time Value" --- p.8 / Chapter 1.2.1 --- Duration --- p.8 / Chapter 1.2.2 --- Qualitative Properties of Duration --- p.10 / Chapter 1.2.3 --- Convexity --- p.16 / Chapter 1.2.4 --- Literatures Review of Duration and Convexity --- p.17 / Chapter 1.2.5 --- Time Value --- p.20 / Chapter 2 --- Management of Interest Rate Risk --- p.22 / Chapter 2.1 --- Laddered Strategy --- p.23 / Chapter 2.2 --- Dumbbell Strategy --- p.24 / Chapter 2.3 --- Immunization Strategy --- p.25 / Chapter 2.4 --- Consideration of Convexity for Managing Interest Rate Risk --- p.26 / Chapter 2.5 --- Duration Targeting[l2] --- p.28 / Chapter 2.6 --- Immunizing Default-Free Bond Portfolios with a Duration Vec- tor [2] --- p.29 / Chapter 2.7 --- The need of Dynamic Global Portfolio Immunization Theorem --- p.32 / Chapter 3 --- Multi-Period Portfolio Selection --- p.34 / Chapter 3.1 --- Objective --- p.34 / Chapter 3.2 --- Dynamic Programming Formulation --- p.35 / Chapter 3.3 --- Specific Situation --- p.46 / Chapter 3.4 --- Summary of Implementation Results --- p.59 / Chapter 4 --- Summary --- p.64 / Bibliography --- p.67 / A Matlab Program of the Dynamic Portfolio Selection --- p.69

Li Chin Pang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 64-66). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Structural Models of Credit Risk --- p.7 / Chapter 2.1 --- Barrier-Independent Models --- p.8 / Chapter 2.2 --- Barrier-Dependent Models --- p.9 / Chapter 2.3 --- Empirical Literature --- p.10 / Chapter 3 --- Jump-Diffusion Models --- p.13 / Chapter 3.1 --- Analytical Option Pricing Formula --- p.14 / Chapter 3.1.1 --- The Jump-Diffusion Model of Merton --- p.14 / Chapter 3.1.2 --- The Jump-Diffusion Model of Kou --- p.15 / Chapter 3.2 --- Simulation for Options --- p.19 / Chapter 3.2.1 --- Simulation for Barrier-Independent Options --- p.19 / Chapter 3.2.2 --- Brownian Bridge Simulation for DOC Option --- p.20 / Chapter 4 --- Likelihood Function for Equity Returns --- p.24 / Chapter 4.1 --- Likelihood Function on Equity Return --- p.26 / Chapter 4.2 --- Degeneracy Problem of Likelihood Function --- p.27 / Chapter 5 --- The Proposed Framework --- p.31 / Chapter 5.1 --- Penalized Likelihood Estimation --- p.31 / Chapter 5.2 --- Expectation-Maximization Algorithm --- p.36 / Chapter 5.3 --- The MJD Structural Model --- p.41 / Chapter 5.4 --- The K<JD Structural Model --- p.43 / Chapter 5.5 --- Computation of the E-step --- p.47 / Chapter 6 --- Performance of Estimation --- p.49 / Chapter 6.1 --- Simulation Checks --- p.49 / Chapter 6.2 --- Empirical Performance --- p.55 / Chapter 6.2.1 --- Bond Selection --- p.55 / Chapter 6.2.2 --- Empirical Results --- p.57 / Chapter 7 --- Conclusion --- p.62 / Bibliography --- p.64

Shen Ruijun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 72-74). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Portfolio Selection Problem --- p.1 / Chapter 1.1.1 --- The Mean-Variance Approach --- p.1 / Chapter 1.1.2 --- The Utility Function Approach --- p.2 / Chapter 1.2 --- Conic Programming and Duality Theory --- p.3 / Chapter 1.2.1 --- Cones and Conic Programming --- p.3 / Chapter 1.2.2 --- Second Order Cones --- p.4 / Chapter 1.3 --- Uncertainties and Robust Optimization --- p.5 / Chapter 1.4 --- Problem Formulation --- p.8 / Chapter 1.4.1 --- Utility Approach Based on a Single-Stage Tree --- p.8 / Chapter 1.4.2 --- Utility Approach Based on a Two-St age Tree --- p.10 / Chapter 1.4.3 --- Robust Counterpart of the Single-Stage Model --- p.14 / Chapter 1.4.4 --- Robust Counterpart of the Two-Stage Model --- p.16 / Chapter 2 --- Single-Stage Robust Selection --- p.20 / Chapter 2.1 --- A Specific Model --- p.20 / Chapter 2.1.1 --- Assumptions --- p.20 / Chapter 2.1.2 --- Formulation of the Model --- p.21 / Chapter 2.1.3 --- Solution for the Model --- p.22 / Chapter 2.2 --- The General Model --- p.26 / Chapter 2.2.1 --- Assumptions --- p.26 / Chapter 2.2.2 --- Solving the model --- p.27 / Chapter 3 --- Results on Two-Stage Models --- p.30 / Chapter 3.1 --- A Specific Two-Stage Robust Model --- p.30 / Chapter 3.1.1 --- Assumptions --- p.30 / Chapter 3.1.2 --- Formulation of the model --- p.32 / Chapter 3.1.3 --- Solution for the Model --- p.33 / Chapter 3.2 --- The General Two-Stage Robust Model --- p.40 / Chapter 3.2.1 --- Assumptions --- p.40 / Chapter 3.2.2 --- Solution for the Model --- p.41 / Chapter 3.2.3 --- General Model with Ellipsoidal Uncertainty Sets --- p.45 / Chapter 4 --- Numerical Results --- p.53 / Chapter 4.1 --- Scenario Tree Generation --- p.53 / Chapter 4.2 --- Numerical Results for the problem (SRP2) --- p.56 / Chapter 5 --- Conclusion --- p.67 / Chapter A --- Equation Derivation --- p.69 / Bibliography --- p.72

現代風險管理需要對金融產品的相關結構做出刻畫，而在實際生活中，我們通常使用相關係數和自相關係數去刻畫這種結構。然而，越來越多的人意識到自相關函數在度量相關結構上面被高估了，特別是在風險管理中我們更關心極端事件。同樣的，偏自相關函數也有這樣的短板。在這篇論文中，我們在有限維分佈服從有正尾係數的正則變差的嚴平穩過程上定義了Partial Extremogram。 這個指標僅僅依賴於隨機過程中的極端值。我們給出了它的一個估計并且研究了這個估計的漸進性質。此外，为了刻畫时间序列的負相關結構，我們把 Inverse Tail Dependence 的想法推廣到了隨機過程上面並且引入了Inverse Extremogram 的概念。我們給出了Inverse Extremogram 在ARMA模型中的顯示表達式。理論推導和數據模擬都說明這個指標可以很好的刻畫出一個隨機過程的尾部的負相關結構。 / Modern risk management calls for deeper understanding of the dependence structure of financial products, which is usually measured by correlation or autocorrelation functions. More and more people realized that autocorrelation function is overvalued as a tool to measure dependence, especially when one has to deal with extremal events in risk management. Likewise, partial autocorrelation function also suffers similar shortcomings as autocorrelation function. In this thesis, an analog of the partial autocorrelation function for a strictly stationary sequence of random variables whose finite-dimensional distributions are jointly regularly varying with positive index, the partial extremogram, is introduced. This function only depends on the extremal events of the underlying process. A natural estimator of the partial extremogram is also proposed and its asymptotic properties are studied. Furthermore, to measure the negative dependence of a time series, the idea of inverse tail dependence is extended to a stochastic process and the notion of inverse extremogram is proposed. A closed form of the inverse extremogram for an ARMA model is deduced. The theoretical and simulation results show that the inverse extremogram is a useful tool for measuring the negative tail dependence of a process. / Detailed summary in vernacular field only. / Chen, Pengcheng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 53-56). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Tail Dependence --- p.2 / Chapter 1.2 --- Extremogram --- p.4 / Chapter 1.2.1 --- Regularly Varying Time Series --- p.4 / Chapter 1.2.2 --- Extremogram for Regularly Varying Time Series --- p.7 / Chapter 1.3 --- Motivation and Organization --- p.8 / Chapter 2 --- Partial Extremogram --- p.9 / Chapter 2.1 --- Definition of Partial Extremogram --- p.9 / Chapter 2.2 --- Applications of Partial Extremogram --- p.15 / Chapter 2.2.1 --- AR(1) Process --- p.15 / Chapter 2.2.2 --- MA(1) process --- p.17 / Chapter 2.2.3 --- Stochastic Volatility Model --- p.19 / Chapter 2.3 --- Estimation of Partial Extremogram --- p.19 / Chapter 2.4 --- Simulation Study --- p.22 / Chapter 3 --- Inverse Extremogram --- p.28 / Chapter 3.1 --- Definition of Inverse Extremogram --- p.28 / Chapter 3.2 --- Applications of Inverse Extremogram --- p.29 / Chapter 3.2.1 --- MA(q) Model --- p.29 / Chapter 3.2.2 --- MA(∞) Model --- p.35 / Chapter 3.2.3 --- ARMA Model --- p.40 / Chapter 3.2.4 --- GARCH Model and SV Model --- p.41 / Chapter 3.3 --- Simulation Study --- p.42 / Chapter 4 --- Conclusions and Further Research --- p.50 / Bibliography --- p.53

Yang, Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 100-106). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Literature review --- p.1 / Chapter 1.2 --- The main contribution of this thesis --- p.5 / Chapter 1.3 --- Relations between the above three models --- p.7 / Chapter 2 --- Model 1 --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Minimax rule risk function --- p.11 / Chapter 2.3 --- Fuzzy liquidity of asset --- p.12 / Chapter 2.4 --- Notations --- p.15 / Chapter 2.5 --- Model formulation --- p.16 / Chapter 2.6 --- Numerical example and result --- p.25 / Chapter 3 --- Model 2 --- p.36 / Chapter 3.1 --- Introduction --- p.36 / Chapter 3.2 --- Notations --- p.39 / Chapter 3.3 --- Model formulation --- p.41 / Chapter 3.4 --- Numerical example and result --- p.45 / Chapter 4 --- Model 3 --- p.51 / Chapter 4.1 --- Introduction --- p.51 / Chapter 4.2 --- Notations --- p.52 / Chapter 4.3 --- Model formulation --- p.54 / Chapter 4.4 --- Numerical example and result --- p.62 / Chapter 5 --- Conclusion --- p.68 / Chapter A --- Source Data for Model 1 --- p.71 / Chapter B --- Source Data for Model 2 --- p.80 / Chapter C --- Source Data for Model 3 --- p.90 / Bibliography --- p.100

Since Markowitz published his seminal work on mean-variance portfolio selection in 1952, almost all literatures in the past half century adhere their investigation to a binding budget spending assumption in static problem settings and a self financing assumption in dynamic settings. In the mean-variance world for a market of all risky assets, however, the common belief of monotonicity does not hold, i.e., not the larger amount you invest, the larger expected future wealth you can expect for a given risk (variance) level. We introduce in this thesis the concept of pseudo efficiency to remove from the candidates such efficient mean-variance policies which can be achieved by less initial investment level. By relaxing the binding budget spending restriction in investment, we derive an optimal scheme in managing initial wealth which dominates the traditional mean-variance efficient frontier. Moreover, as the general 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 have incentives to deviate from the pre-committed optimal mean-variance portfolio policy during the investment process under certain circumstances. By introducing the concept of time inconsistency in efficiency and defining the induced trade-off, we further demonstrate in this thesis that investors 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 a revised dynamic mean-variance policy for a market with a riskless asset 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 (FCFS) during the investment process. We further apply the concept of pseudo efficiency to a dynamic market of all risky assets and explore (better) revised dynamic mean-variance policies. By including the free cash flow stream in the total wealth, our proposed policy dominates the pre-committed optimal mean-variance portfolio policy in the sense that while both achieve the same total mean, the revised policy generates a smaller total variance. We reveal in this thesis that the time consistency in efficiency is closely related to the completeness of the market. We further discuss the relationship between time consistency in efficiency and the variance-optimal signed martingale measure (VSMM) of the market. Finally we show that time inconsistency in efficiency can be eliminated by enforcing no-shorting constraint for some market setting. / Cui, Xiangyu. / Adviser: Li Duan. / Source: Dissertation Abstracts International, Volume: 72-04, Section: A, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 163-170). / 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 second is a. project management problem with task subcontracting. The project owner (P0) outsources the tasks in his project to different subcontractors (SCs), with contracts to govern the completions of the tasks and the associated costs and bonus. We model the subcontractors' task processing problem as a Cooperative Game so that subcontractors can benefit by resource sharing and execution time rescheduling. We prove that our cooperative game is balanced and propose a core allocation vector constructed from the optimal dual solution. Meanwhile, the project owner's optimal strategy to design the contracts is also obtained by implicit optimization skills. / The third problem we consider concerns about manufacturing outsourcing, where multiple manufacturers outsource their jobs to a third-party firm. The manufacturers book time windows from the third-party to process their jobs whose processing times are stochastic. Due to the capacity limitation of the third-party and the uncertainty in their processing times, it may be beneficial for the manufacturers to cooperate, provided that a proper cooperative mechanism can be devised. We model this problem as a Cooperative Game. However, it is more than a Sequencing Game commonly studied in the literature, because we consider the optimal booking decisions and the random processing times, which make it possible for the manufacturers to achieve a risk pooling effect by collaborating and booking together. We prove that the outsourcing game is balanced in the situation where the unit booking cost for each time window is unique. We also construct a core allocation based on the core vector derived form a Permutation Game. A main breakthrough is that the connective admissible rearrangement assumption is removed for the stochastic sequencing/booking game, following Slikker's technique. / This thesis investigates three problems in operations management, by using different concepts and techniques in Game Theory. The first problem is a two-echelon supply chain problem involving wholesaling, transporting and retailing of certain kind of perishable product. A key characteristic of the problem is that the upstream supplier adopts a. Group Buying Scheme (GBS) as his pricing mechanism and the downstream retailers, taking into consideration of the supplier's pricing mechanism, their respective market demands and other retailers' likely reactions, compete with each other to maximize their profit respectively. We model this problem as a. Stackberg game where supplier is the leader and retailers are the followers. Furthermore, the retailers' optimal ordering problem is solved by applying the solution concepts in Competition Game Theory and we prove that the Nash equilibrium always exists. Moreover, the equilibrium is the only Pareto optimal Nash equilibrium and a strong equilibrium as well. Finally we show that the GBS pricing mechanism, as compared with the traditional Flat Price scheme, can bring the supplier and retailers to a win-win situation. / Zhang, Feng. / Adviser: Xianqiang Cai. / Source: Dissertation Abstracts International, Volume: 73-02, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 136-140). / 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.

Mean-variance criterion in optimization AL problem aims at maximizing the final surplus; asset value minus liability value, subject to a given variance of the final surplus or, equivalently, minimizing the variance of the final surplus subject to a given expected final surplus. The stochastic optimal control theory is employed to analytically solve the AL management problem in continuous-time setting. Then the comparison of derived optimal AL management policy and the literatures are examined and the discrepancy in objectives between equity holders and investors of a mutual fund is discussed finally. / Portfolio selection in asset-liability (AL) management is to seek the best allocation of wealth among a basket of securities with taking into account the liabilities. There are a lot of portfolio selection criteria among in the literature. The two of them are mean-variance criterion and Roy's safety-first principle. This thesis investigates the optimal asset allocation for an investor who is facing an uncontrollable liability under either one of these two portfolio constructions. The relation between these two different principles are discussed in the context of AL management. / Roy's safety-first principle (Roy, 1956) asserts that the investor would specify a threshold level of the final surplus below which the outcome is regarded as disaster. The objective is then to minimize the ruin probability or the chance of disaster subject to a constraint that the expected final surplus is higher than the threshold. Roy however solves this problem by minimizing an upper bound of the ruin probability based on the Bienayme-Chebycheff inequality. With the same consideration of Roy, the analytical trading strategy of the safety-first. AL management, problem, in the sense of surplus, under both continuous- and multi-period-time settings are derived. We link this surrogated safety-first principle to the mean-variance ones. / The final objective of this thesis attacks the genuine safety-first AL problem. Without replacing the ruin probability in the objective function by its upper bound, we use a martingale approach and consider the funding ratio which is the total wealth divided by the total liability. Two important situations in the literature are investigated. In the first situation, the mean constraint of the original problem is removed, We show that removing the mean constraint makes the problem become a target reaching problem that can be solved analytically. However, the essence of safety-first is lost. In the second case in which the mean constraint is there, the problem becomes ill-posed and is then solved using an approximation using a martingale approach. The approximation relies on the assumption that the investor gives up unreasonably high profits and sets an upper bounded for the final funding ratio. / Chiu, Mei Choi. / "July 2007." / Adviser: Duan Li. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1304. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 121-126). / 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, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.