by Siu-ming Cha. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 123-132). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Objective --- p.1 / Chapter 1.2 --- Problem --- p.1 / Chapter 1.2.1 --- Motivation --- p.1 / Chapter 1.2.2 --- Approaches --- p.3 / Chapter 1.3 --- Contributions --- p.4 / Chapter 1.4 --- Organization of this Thesis --- p.5 / Chapter 2 --- Independent Component Analysis --- p.8 / Chapter 2.1 --- Overview --- p.8 / Chapter 2.2 --- The Blind Source Separation Problem --- p.8 / Chapter 2.3 --- Statistical Independence --- p.10 / Chapter 2.3.1 --- Definition --- p.10 / Chapter 2.3.2 --- Measuring Independence --- p.11 / Chapter 2.4 --- Developments of ICA Algorithms --- p.15 / Chapter 2.4.1 --- ICA Algorithm: Removal of Higher Order Dependence --- p.16 / Chapter 2.4.2 --- Assumptions in ICA Algorithms --- p.19 / Chapter 2.4.3 --- Joint Approximate Diagonalization of Eigenmatrices(JADE) --- p.20 / Chapter 2.4.4 --- Fast Fixed Point Algorithm for Independent Component Analysis(FastICA) --- p.21 / Chapter 2.5 --- Principal Component Analysis and Independent Component Anal- ysis --- p.23 / Chapter 2.5.1 --- Theoretical Comparisons between ICA and PCA --- p.23 / Chapter 2.5.2 --- Comparisons between ICA and PCA through a Simple Example --- p.24 / Chapter 2.6 --- Applications of ICA in Finance: A review --- p.27 / Chapter 2.6.1 --- Relationships between Cocktail-Party Problem and Fi- nance --- p.27 / Chapter 2.6.2 --- Security Structures Explorations --- p.28 / Chapter 2.6.3 --- Factors Interpretation and Visual Analysis --- p.29 / Chapter 2.6.4 --- Time Series Prediction by Factors --- p.29 / Chapter 2.7 --- Conclusions --- p.30 / Chapter 3 --- Factor Models in Finance --- p.31 / Chapter 3.1 --- Overview --- p.31 / Chapter 3.2 --- Factor Models and Return Generating Processes --- p.32 / Chapter 3.2.1 --- One-Factor Model --- p.33 / Chapter 3.2.2 --- Multiple-Factor Model --- p.34 / Chapter 3.3 --- Abstraction of Factor Models in Portfolio --- p.35 / Chapter 3.4 --- Typical Applications of Factor Models: Portfolio Mangement --- p.37 / Chapter 3.5 --- Different Approaches to Estimate Factor Model --- p.39 / Chapter 3.5.1 --- Time-Series Approach --- p.39 / Chapter 3.5.2 --- Cross-Section Approach --- p.40 / Chapter 3.5.3 --- Factor-Analytic Approach --- p.41 / Chapter 3.6 --- Conclusions --- p.42 / Chapter 4 --- ICA and Factor Models --- p.43 / Chapter 4.1 --- Overview --- p.43 / Chapter 4.2 --- Relationships between BSS and Factor Models --- p.43 / Chapter 4.2.1 --- Mathematical Deviation from Factor Models to Mixing Process --- p.45 / Chapter 4.3 --- Procedures of Factor Model Constructions by ICA --- p.47 / Chapter 4.4 --- Sorting Criteria for Factors --- p.48 / Chapter 4.4.1 --- Kurtosis --- p.50 / Chapter 4.4.2 --- Number of Runs --- p.52 / Chapter 4.5 --- Experiments and Results I: Factor Model Constructions --- p.53 / Chapter 4.5.1 --- Factors and their Sensitivities Extracted by ICA --- p.55 / Chapter 4.5.2 --- Factor Model Construction for a Stock --- p.60 / Chapter 4.6 --- Discussion --- p.62 / Chapter 4.6.1 --- Remarks on Applying ICA to Find Factors --- p.62 / Chapter 4.6.2 --- Independent Factors and Sparse Coding --- p.63 / Chapter 4.6.3 --- Selecting Securities for ICA --- p.63 / Chapter 4.6.4 --- Factors in Factor Models --- p.65 / Chapter 4.7 --- Conclusions --- p.66 / Chapter 5 --- Factor Model Evaluations and Selections --- p.67 / Chapter 5.1 --- Overview --- p.67 / Chapter 5.2 --- Random Residue: Requirement of Independent Factor Model --- p.68 / Chapter 5.2.1 --- Runs Test --- p.68 / Chapter 5.2.2 --- Interpretation of z-value --- p.70 / Chapter 5.3 --- Experiments and Results II: Factor Model Selections --- p.71 / Chapter 5.3.1 --- Randomness of Residues using Different Sorting Criteria --- p.71 / Chapter 5.3.2 --- Reverse Sortings of Kurtosis and Number of Runs --- p.76 / Chapter 5.4 --- Experiments and Results using FastICA --- p.80 / Chapter 5.5 --- Other Evaluation Criteria for Independent Factor Models --- p.85 / Chapter 5.5.1 --- Reconstruction Error --- p.86 / Chapter 5.5.2 --- Minimum Description Length --- p.89 / Chapter 5.6 --- Conclusions --- p.92 / Chapter 6 --- New Applications of Independent Factor Models --- p.93 / Chapter 6.1 --- Overview --- p.93 / Chapter 6.2 --- Applications to Financial Trading System --- p.93 / Chapter 6.2.1 --- Modifying Shocks in Stocks --- p.96 / Chapter 6.2.2 --- Modifying Sensitivity to Residue --- p.100 / Chapter 6.3 --- Maximization of Higher Moment Utility Function --- p.104 / Chapter 6.3.1 --- No Good Approximation to Utility Function --- p.107 / Chapter 6.3.2 --- Uncorrelated and Independent Factors in Utility Ma mizationxi- --- p.108 / Chapter 6.4 --- Conclusions --- p.110 / Chapter 7 --- Future Works --- p.111 / Chapter 8 --- Conclusion --- p.113 / Chapter A --- Stocks used in experiments --- p.116 / Chapter B --- Proof for independent factors outperform dependent factors in prediction --- p.117 / Chapter C --- Demixing Matrix and Mixing Matrix Found by JADE --- p.119 / Chapter D --- Moments and Cumulants --- p.120 / Chapter D.1 --- Moments --- p.120 / Chapter D.2 --- Cumulants --- p.121 / Chapter D.3 --- Cross-Cumulants --- p.121 / Bibliography --- p.123

The maximum drawdown on a time interval [0, T] of a random process can be defined as the largest drop from a high water mark to a low water mark. In this project, expected maximum drawdowns are analyzed in two cases: maximum drawdowns under constant volatility and stochastic volatility. We consider maximum drawdowns of both generalized and geometric Brownian motions. Their paths are numerically simulated and their expected maximum drawdowns are computed using Monte Carlo approximation and plotted as a function of time. Only numerical representation is given for stochastic volatility since there are no analytical results for this case. In the constant volatility case, the asymptotic behavior is described by our simulations which are supported by theoretical findings. The asymptotic behavior can be logarithmic for positive mean return, square root for zero mean return, or linear for negative mean return. When the volatility is stochastic, we assume it is driven by a mean-reverting process, in which case we discovered that if one uses the effective volatility in the formulas obtained for the constant volatility case, the numerical results suggest that similar asymptotic behavior holds in the stochastic case.

One major criticism about the traditional mean-variance portfolio optimization is that it tends to magnify the estimation error. A little estimation error can cause the distortion of the whole portfolio. Two popular ways to solve this problem are to use a resampling method or the Black-Litterman method (Bayesian method). The clustering method is a newer way to solve the problem. Clustering means we group the highly correlated stocks first and treat the group as a single stock. After we group the stocks, we will have some clusters of stocks, then we run the traditional mean-variance portfolio optimization for these clusters. The clustering method can improve the stability of the portfolio and reduce the impact of estimation error. In this project, we will explain why it works and we will perform tests to determine if clustering methods do improve the stabilities and performance of the portfolio.

Calculation of the Value at Risk (VaR) measure, of a portfolio, can be done using Monte Carlo simulations of that portfolio's potential losses over a specified period of time. Regulators, such as the US Securities and Exchange Commission, and Exchanges, such as the New York Stock Exchange, establish regulatory capital requirements for firms. These regulations set the amount of capital that firms are required to have on hand to safeguard against market loses that can occur. VaR gives us this specific monetary value set by Regulators and Exchanges. The specific amount of capital on hand must satisfy that, for a given confidence level, a portfolio's loses over a certain period of time, will likely be no greater than the capital required a firm must have on hand. The scenario used will be one of a Risk Manager position in which this manager inherited a portfolio that was set up for a client beginning in April 1992. The portfolio will have to meet certain parameters. The initial portfolio is worth $61,543,328.00. The risk manager will be responsible for the calculation of the Value at Risk measure, at five percent, with a confidence level of 95% and 20 days out from each of the 24 business quarters, over a six year period, starting in 1992 and ending in 1996.

A gestão de clientes é um processo que envolve a tomada de decisões estratégicas, que influenciam a composição do portfólio de clientes da companhia, e operacionais, que afetam o relacionamento dos clientes com a empresa no dia a dia. O framework sugerido nesta tese propicia a integração dessas duas perspectivas, permitindo aos gestores alocarem melhor os recursos de marketing, por possibilitarem (a) o incremento da eficiência da carteira de clientes, a partir da sua otimização, e (b) a identificação dos clientes mais propensos a gerarem lucros futuros, com base na modelagem de customer lifetime value (CLV) desenvolvida. A abordagem de otimização do portfólio de clientes foi elaborada para auxiliar os gestores a definirem os segmentos que devem ser alvo dos investimentos de marketing e tem como objetivo indicar a composição da carteira de clientes que proporcionará a rentabilidade, a diversificação do risco e a lucratividade desejadas pelos acionistas. A abordagem sugerida é uma adaptação para o marketing da teoria financeira do portfólio. Foram incluídas restrições específicas para a área de gestão de clientes que asseguram a exequibilidade dos portfólios recomendados, tanto em relação à necessidade de aquisição de clientes ou de redução da participação dos segmentos na carteira, quanto em relação à manutenção da lucratividade da empresa. Ademais, foram incorporadas opções de estimação do retorno, tais como a inclusão da tendência à série com base na modelagem SUR, além de serem avaliadas a utilização de duas proxies para o risco, a variância e o Conditional Value at Risk. De acordo com o framework de gestão de clientes proposto, a implementação das decisões estratégicas é viabilizada a partir da integração da análise dos resultados obtidos pela otimização com a avaliação proporcionada pelo modelo de CLV sugerido. Este, além de englobar a evolução do comportamento do cliente ao longo do relacionamento da empresa, considera o retorno e a matriz de probabilidade de troca de segmento de maneira individualizada. A heterogeneidade da matriz de Markov foi alcançada a partir da combinação convexa da matriz de transição geral com a matriz personalizada de cada cliente, possibilitando, assim, a priorização de clientes pertencentes a um mesmo segmento. O framework sugerido foi aplicado na base de clientes de uma grande empresa que atua nacionalmente na indústria de serviços financeiros. Após a constatação de que os segmentos podem gerar diferentes retornos e representar distintos níveis de risco para a companhia, foi feita a comparação dos resultados dos portfólios recomendados com o realizado. Os portfólios sugeridos desempenharam melhor de maneira consistente em termos de lucratividade e de eficiência, medida a partir do sharpe ratio. Em relação ao modelo de CLV, os resultados foram comparados com os obtidos a partir do modelo de Pfeifer & Carraway (2000), utilizado como ponto de partida para o seu desenvolvimento. As modificações incorporadas, além de possibilitarem a individualização por cliente, aumentaram a precisão da previsão dos valores individuais e a qualidade do ordenamento, mantendo a capacidade de avaliação do valor da base. Para resumir, foi proposto um framework de gestão de clientes que inclui a avaliação do risco, possibilitando aos gestores uma visão holística do negócio e particular de cada cliente. / Customer management is a process that involves strategic decision-making, which influence the composition of the customer portfolio, and operational decision making, which affect the relationship of each customer with the company. The proposed framework provides the integration of the strategic and operational perspectives, empowering managers to better allocate marketing resources as it enables (a) the increase of the efficiency of the customer portfolio, through its optimization, and (b) the identification of the customers that are more likely to bring profit in the future, through the customer lifetime value (CLV) model developed. The customer portfolio optimization method was built to help managers to define the customer segments that should be the target of their marketing investments. Its purpose is to indicate the customer portfolio composition that will provide the return, profitability and risk diversification desired by shareholders. The suggested approach is an adaptation to marketing of financial portfolio theory. In this way, customer management specific constrains were included to ensure the applicability of the recommended portfolios in terms of either the necessity of acquiring new customers or reducing the importance of a given segment in the portfolio as well as in terms of maintaining the company’s profitability. Furthermore, options of estimating return were incorporated such as the inclusion of the trend in the time series based SUR modeling as well as the optimizations were evaluated considering two proxies for risk, variance and Conditional Value at Risk. According to the proposed framework, the implementation of the strategic decisions concerning the changes needed in the customer portfolio become possible through the integration of the results of the optimization with the estimation of the value of each customer provided by the CLV model developed. In this model, besides accounting for the evolution of the customer behavior throughout the duration of his relationship with the company, we also consider, for each customer, his individual return and his individual transition matrix. The heterogeneity of the Markov matrix was reached with a convex combination of the general transition matrix and the personalized matrix of each customer. It, therefore, enables managers to priorize customers of the same segment. The suggested framework was applied to the customer database of a large national company from the financial services industry. Once evidenced that the customer segments can generate different returns and can have different levels of risk for the company, we compared the results of the recommended with the current. The portfolios suggested by the optimization performed consistently better in terms of profitability and efficiency, measured through sharpe ratio. Concerning the CLV model developed, we compared the results with Pfeifer & Carraway (2000) model, which was used as the start point for our model. The improvements implemented not only allowed the estimation of CLV at the individual level, but also increased the precision of the predictions for the customer lifetime values and for the customer ranking, maintaining the quality of the customer equity forecast. To sum up, our proposed framework which includes risk assessment enables marketing managers to have a holistic vision of their customer portfolio and to drilldown into a particular vision of each customer.

Este estudo se propõe analisar como as organizações utilizam a gestão de portfólio de projetos para gerir a inovação. Para tanto, busca explorar como as organizações identificam, categorizam, classificam, selecionam e priorizam os projetos, e como controlam e medem os resultados de seu portfólio de inovação, em um contexto contendo projetos de diferentes naturezas de inovação. Para atingir este objetivo foi realizada uma pesquisa qualitativa, através de seis entrevistas em profundidade. O roteiro de entrevista foi criado a partir do estudo do modelo de gestão de portfólio proposto pelo PMI (2013) e revisado por três especialistas. Para esta pesquisa foram entrevistadas três empresas, sendo dois profissionais por empresa, um de cargo gerencial e outro de cargo executivo, ligados à gestão de portfólio de inovação. As entrevistas foram analisadas quanto ao seu conteúdo através da análise temática. A análise das entrevistas é apresentada a partir de quatro grandes temas: o contexto da gestão de portfólio de inovação na organização, o processo de avaliação e seleção de projetos para o portfólio, o processo de monitoramento do portfólio e os desafios da gestão de portfólios de inovação. Como resultados, a pesquisa identificou que as empresas pesquisadas têm como base de influência principal o modelo de gestão de portfólio proposto pelo PMI (2013), além de outros métodos como Stage-gate, Corrente Crítica, Lean, OKR e PDCA. Que as organizações buscam adaptar o processo de gestão de portfólio à sua realidade e são feitas adaptações de acordo com a complexidade do portfólio de projetos de inovação da organização, conforme a natureza das inovações presente nos projetos do portfólio, sua ambição de inovação e os desafios encontrados na implementação da gestão de seu portfólio de inovação; que são utilizadas diferentes técnicas de avaliação de viabilidade de projetos, com o uso do modelo Stage-gate, facilitando a seleção de projetos para o portfólio, de acordo com o grau de incerteza dos projetos; que são utilizadas técnicas como a Corrente Crítica para priorizar o portfólio e reduzir o lead time de projetos, reduzindo o tempo para iniciar a captura de valor advindo destes; que a qualidade do processo de monitoramento do portfólio está ligada diretamente à qualidade do processo de categorização dos projetos e de seus descritores-chave; que a resistência gerencial em reportar desempenho dos projetos é um desafio para as organizações; e, por fim, que todas as organizações reforçam seus processos de gestão de portfólio de inovação de acordo com suas ambições de inovação e de acordo com sua maturidade quanto a importância da inovação para a empresa, de onde se pode sugerir que as organizações com gestão de portfólio mais rígida e formalizada são também as organizações menos inovadoras. / This study aims to analyze how organizations use project portfolio management to manage innovation. To do so, it seeks to explore how organizations identify, categorize, classify, select and prioritize their projects, and control and measure the results of their innovation portfolio, in a context containing projects of different natures of innovation. To achieve this goal, a qualitative research was conducted through in-depth interviews. The interview script was created based on the study of the portfolio management model proposed by PMI (2013) and reviewed by three specialists. For this research, three companies were interviewed, two professionals per company, one managerial and one executive, both linked to innovation portfolio management at their organizations. The interviews were analyzed for their content through thematic analysis. The analysis of the interviews is presented based on four main themes: the context of portfolio management innovation in the organization; the project evaluation and selection processes for the portfolio; the portfolio monitoring process; and the innovation portfolio management challenges. As a result, it was identified that the companies surveyed are influenced by PMI's (2013) portfolio management model, as well as other complementary methods such as Stage-gate, Critical Current, Lean, OKR and PDCA; that the organizations seek to adapt the portfolio management process to their reality, and that adaptations are made according to the complexity of the organization's innovation portfolio, according to the nature of innovations present in the portfolio projects, according to its innovation ambition and according to the challenges encountered in implementing the management of its innovation portfolio; that different project feasibility evaluation techniques are used, with the use of the Stage- Gate model, facilitating the selection of projects for the portfolio, according to the degree of uncertainty of the projects; that techniques such as the Critical Chain are used to prioritize the portfolio and reduce the lead time of projects, reducing the time to start capturing value from them; that the quality of the portfolio monitoring process is directly linked to the quality of the project categorization process and its key descriptors; that the managerial resistance to reporting project performance is a challenge; and lastly, that all organizations reinforce their innovation portfolio management processes according to their innovation ambitions and according to their maturity about the importance of innovation for the company, suggesting that organizations with more rigid and formalized portfolio management are also less innovative organizations.

As we know, the deterministic LQ problems are well-posed if the state weighting matrix and the control weighting matrix are nonnegative and positive definite in the cost function, respectively. Some practical problems, however, often include indefinite weighting matrices in their cost functions such as mean-variance portfolio selection problem. This inspires us to further study the indefinite LQ problems in detail. / In this thesis, we study indefinite stochastic linear-quadratic (LQ) control with jumps and present some financial applications of this new development. / The results of the above LQ control problems are employed to deal with a mean-variance portfolio selection model in an incomplete financial market. An optimal analytical investment strategy is directly derived and the expression of its risk is explicitly presented. In addition, a mean-variance portfolio selection model in a financial market where shorting is not allowed is investigated in detail via the stochastic LQ problem with nonnegative controls. In particular, the explicit expression of the efficient frontier enables an investor to better understand the relation between the expected terminal wealth and the risk in a stock market with no-shorting. / The weighting matrices in the cost function are allowed to be indefinite (in particular, negative) when the diffusion term linearly depends on the control variable in the state equation. In this case, indefinite stochastic LQ control problems with jumps may still be sensible and well-posed. In an infinite time horizon, solvability of coupled generalized algebraic Riccati equations (CGAREs) is sufficient for the well-posedness of the stochastic LQ control problem with jumps. Moreover, an approach algorithm is devised to solve the CGAREs via semi-definite programming over linear matrix inequalities. On the other hand, it is shown that the well-posedness of the stochastic LQ control problem in a finite time horizon with jumps is equivalent to solvability of coupled generalized Riccati equations. / Li Xun. / "November 2000." / Advisers: Cai Xiaoqiang; Zhou Xunyu. / Source: Dissertation Abstracts International, Volume: 61-10, Section: B, page: 5541. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 115-122). / 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.

Chen Li. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 76-78). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Table of Contents --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature review --- p.4 / Chapter 3 --- The semi-mean target tracking model --- p.9 / Chapter 3.1 --- Introduction --- p.9 / Chapter 3.2 --- The robust optimization problem --- p.11 / Chapter 3.3 --- Portfolio selection methods --- p.14 / Chapter 3.3.1 --- Jensen's inequality approach --- p.15 / Chapter 3.3.2 --- The robust optimization approach --- p.17 / Chapter 3.3.3 --- Empirical method --- p.22 / Chapter 3.4 --- How to evaluate a portfolio? --- p.24 / Chapter 3.4.1 --- Tight bounds --- p.24 / Chapter 3.4.2 --- The semidefinite programming bounds --- p.25 / Chapter 3.4.3 --- Conclusions --- p.28 / Chapter 3.5 --- Numerical results --- p.29 / Chapter 3.5.1 --- The analysis of the data --- p.29 / Chapter 3.5.2 --- Jensen's inequality approach --- p.31 / Chapter 3.5.3 --- The robust optimization approach --- p.34 / Chapter 3.5.4 --- The empirical linear programming method --- p.34 / Chapter 3.6 --- Comparisons and conclusions --- p.39 / Chapter 4 --- The semi-variance target tracking model --- p.45 / Chapter 4.1 --- Introduction --- p.45 / Chapter 4.2 --- The portfolio selection methods --- p.46 / Chapter 4.2.1 --- The robust optimization method --- p.47 / Chapter 4.2.2 --- The empirical method --- p.50 / Chapter 4.3 --- Evaluating a selected portfolio --- p.52 / Chapter 4.3.1 --- Computing SDP bounds --- p.52 / Chapter 4.3.2 --- Conclusions --- p.55 / Chapter 4.4 --- Numerical results --- p.55 / Chapter 4.4.1 --- The robust optimization method --- p.56 / Chapter 4.4.2 --- The empirical second order cone programming method --- p.61 / Chapter 4.4.3 --- Comparisons and conclusions --- p.61 / Chapter 4.5 --- Summary and future work --- p.69 / Appendix A --- p.70 / Bibliography --- p.76

交易员通常在处理大单交易时会遇到困难，因为市场没有足够的流动性来消化这些买单或卖单。交易员想要在对市场产生冲击最小的情况下完成加仓或平仓，或者他们想设计一套程序来达成这个目的。 / 由于每次的交易结果都是一个随机变量，为了方便比较，我们可以设置一个比较基准，在本文中我们选用。 / 本文对之前存在的动态一致性风险测度模型的一大改进是引入了动量效应。在短时的股市中动量效应就有明显效应。 / 我们的最优策略是当市场朝我们不利的方向变动时我们加速仓位的增加或减少，而朝我们有利的方向变动时我们减缓我们的动作。我们的最优策略每期都会出请或买入一个预先设定的比例的股票，同时我们会在交易的初期加快我们的买卖处理，而在后期放缓动作。 / 我们的最优策略是时间一致的，并且是一个动态变化的策略。 / For an equity trader, one problem he faces is to execute large order of stocks for his clients. The trader seeks to optimize his performance for buying and selling stocks. Basically various costs incurred during the trading includes the commission fees, margin loans, bid-ask spread, price impacts, taxes and other occasional costs. But among the all, the price impact takes the largest part. / In a sell program, the implementation shortfall is the differience between the value of the trader’s initial equity position and the sum of the cash flow he receives from his trading process. Because of the randomness inherited in the stock price process, the resulting implementation shortfall is a random variable, and we should project the random variable into real number to compare. The measure we choose is the dynamic coherent risk measure. / One of the most significant improvements of our model is the inclusion of momentum effect. Momentum is a significant effect when considering stock price dynamics in a daily circle. Another main contribution is the approximation method used in solving our model, which helps reduce much computation burden. / Our strategy applies best to the high frequency trading problem due to the nature of our approximation method. The optimal strategy in our framework is to trade more when the current price drift is negative. This is mainly due to the prevention from future possible negative price drifts. Our strategy also shows that, in addition to liquidate a fixed proportion of inventory at each period, the trader has to trade faster at earlier periods.Our optimal strategy derived from dynamic programming is time consistent and is an adapted process. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / He, Mengfei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 132-134). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.10 / Chapter 2.1 --- Model Comparison --- p.10 / Chapter 2.1.1 --- Price dynamics --- p.10 / Chapter 2.1.2 --- Price impacts --- p.11 / Chapter 2.1.3 --- Inventory constraints --- p.14 / Chapter 2.1.4 --- Objective functions and risk measures --- p.15 / Chapter 2.1.5 --- Discrete or continuous framework --- p.17 / Chapter 2.2 --- Work by Bertsimas and Lo --- p.18 / Chapter 2.2.1 --- Formulation under Linear Price Impact --- p.21 / Chapter 2.2.2 --- Formulation under LPT Law --- p.22 / Chapter 2.2.3 --- Formulation under General Price Impact --- p.26 / Chapter 2.2.4 --- Portfolio Case --- p.28 / Chapter 2.3 --- A Series ofWorks by Almgren --- p.29 / Chapter 2.3.1 --- Adaptive Arrival Price --- p.29 / Chapter 2.3.2 --- Bayesian Adaptive Trading with a Daily Cycle --- p.32 / Chapter 2.3.3 --- Mean-Variance Optimal Adaptive Execution --- p.36 / Chapter 2.4 --- Work by Lin and Pena --- p.42 / Chapter 2.4.1 --- Multiple Assets --- p.46 / Chapter 2.5 --- A Series ofWorks by Forsyth --- p.48 / Chapter 2.5.1 --- A Hamilton-Jacobi-Bellman Approach to Optimal Trade Execution --- p.49 / Chapter 2.5.2 --- A Mean Quadratic Variation Approach --- p.55 / Chapter 2.6 --- A Series ofWorks by Schied --- p.58 / Chapter 2.6.1 --- Optimal Trade Execution in Limit Order BookModels --- p.58 / Chapter 2.6.2 --- Optimal Trade Execution under Geometric BrownianMotion --- p.66 / Chapter 2.7 --- Work byMoazeni --- p.69 / Chapter 3 --- Model Setting --- p.71 / Chapter 3.1 --- ExecutionModel --- p.71 / Chapter 3.2 --- Coherent Dynamic RiskMeasures --- p.81 / Chapter 3.3 --- Optimization Formulation --- p.84 / Chapter 4 --- Solution Methodologies --- p.89 / Chapter 4.1 --- BinomialModel --- p.89 / Chapter 4.2 --- Linear Approximation --- p.92 / Chapter 4.3 --- Numerical Results --- p.107 / Chapter 4.4 --- Simulation Results --- p.110 / Chapter 4.5 --- Efficient Frontier --- p.111 / Chapter 4.6 --- CVaR Case --- p.113 / Chapter 5 --- Conclusions and Future Research --- p.119 / Chapter 5.1 --- Conclusions --- p.119 / Chapter 5.2 --- Future Research --- p.121 / Chapter A --- Equation Derivation --- p.124 / Bibliography --- p.132

This thesis studies the equilibrium behavior of continuous-time capital markets with various market assumptions. These assumptions include different settings of the investment opportunity set and consideration of the variability of the number of shares outstanding of stocks and the investment horizons of investors. Two capital asset pricing models (CAPMs) are established for every case. One of these CAPM focuses on the study of the relationship between the terminal rate of return of any given portfolio and the benchmark portfolios. The other CAPM focuses on the instantaneous rate of return. The market portfolios (and their substitutes for some cases) of all market situations are explicitly derived given homogeneous expectations. The mean-variance efficiencies with a specific terminal time are then investigated. It is proved that some of these market portfolios must be inefficient for a non-zero investment horizon. Moreover, the instantaneous efficiency of portfolios is studied for some market situations. The CAPMs are then developed based on the conditions of each market situation. / Chiu Chun Hung. / "December 2003." / Adviser: Xun Yu Zhou. / Source: Dissertation Abstracts International, Volume: 64-11, Section: A, page: 4147. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 185-187). / 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. / Abstracts in English and Chinese. / School code: 1307.