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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.

Sen Sui. / Thesis submitted in: August 2003. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 88-92). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iv / Dedication --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation and Objective --- p.1 / Chapter 1.2 --- Contributions --- p.4 / Chapter 1.3 --- Thesis Organization --- p.5 / Chapter 2 --- Background of Risk Management --- p.7 / Chapter 2.1 --- Measuring Return --- p.8 / Chapter 2.2 --- Objectives of Risk Measurement --- p.11 / Chapter 2.3 --- Simple Statistics for Measurement of Risk --- p.15 / Chapter 2.4 --- Methods for Value-at-Risk Measurement --- p.16 / Chapter 2.5 --- Conditional VaR --- p.18 / Chapter 2.6 --- Portfolio VaR Methods --- p.18 / Chapter 2.7 --- Coherent Risk Measure --- p.20 / Chapter 2.8 --- Summary --- p.22 / Chapter 3 --- Selection of Independent Factors for VaR Computation --- p.23 / Chapter 3.1 --- Mixture Convolution Approach Restated --- p.24 / Chapter 3.2 --- Procedure for Selection and Evaluation --- p.26 / Chapter 3.2.1 --- Data Preparation --- p.26 / Chapter 3.2.2 --- ICA Using JADE --- p.27 / Chapter 3.2.3 --- Factor Statistics --- p.28 / Chapter 3.2.4 --- Factor Selection --- p.29 / Chapter 3.2.5 --- Reconstruction and VaR Computation --- p.30 / Chapter 3.3 --- Result and Comparison --- p.30 / Chapter 3.4 --- Problem of Using Kurtosis and Skewness --- p.40 / Chapter 3.5 --- Summary --- p.43 / Chapter 4 --- Mixture of Gaussians and Value-at-Risk Computation --- p.45 / Chapter 4.1 --- Complexity of VaR Computation --- p.45 / Chapter 4.1.1 --- Factor Selection Criteria and Convolution Complexity --- p.46 / Chapter 4.1.2 --- Sensitivity of VaR Estimation to Gaussian Components --- p.47 / Chapter 4.2 --- Gaussian Mixture Model --- p.52 / Chapter 4.2.1 --- Concept and Justification --- p.52 / Chapter 4.2.2 --- Formulation and Method --- p.53 / Chapter 4.2.3 --- Result and Evaluation of Fitness --- p.55 / Chapter 4.2.4 --- Evaluation of Fitness using Z-Transform --- p.56 / Chapter 4.2.5 --- Evaluation of Fitness using VaR --- p.58 / Chapter 4.3 --- VaR Estimation using Convoluted Mixtures --- p.60 / Chapter 4.3.1 --- Portfolio Returns by Convolution --- p.61 / Chapter 4.3.2 --- VaR Estimation of Portfolio Returns --- p.64 / Chapter 4.3.3 --- Result and Analysis --- p.64 / Chapter 4.4 --- Summary --- p.68 / Chapter 5 --- VaR for Portfolio Optimization and Management --- p.69 / Chapter 5.1 --- Review of Concepts and Methods --- p.69 / Chapter 5.2 --- Portfolio Optimization Using VaR --- p.72 / Chapter 5.3 --- Contribution of the VaR by ICA/GMM --- p.76 / Chapter 5.4 --- Summary --- p.79 / Chapter 6 --- Conclusion --- p.80 / Chapter 6.1 --- Future Work --- p.82 / Chapter A --- Independent Component Analysis --- p.83 / Chapter B --- Gaussian Mixture Model --- p.85 / Bibliography --- p.88

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

In infinitely repeated games, we also give definitions to risk attitude and reputation. As art infinitely repeated game is a repetition of a constituent strategic game, we transform each single round of an infinitely repeated game as a risk game. We extend the definitions of risk strategies and risk strategy equilibrium to infinitely repeated games. We also research some properties of risk strategy equilibrium and show that players can obtain higher payoffs in risk strategy equilibrium than in pure strategy Nash equilibrium. / In multi-agent systems, agents often need to make decisions, especially under uncertainty. When a decision-maker needs to choose among a number of choices, each having a certain probability to happen, one of the traditional ways discussed in economics is to calculate the expected utility of each choice and choose the one with the maximum expected utility. However, most of the humans do not do so in real situations. Very often, humans choose a choice with a lower expected utility. One of the famous examples is the Allais paradox. / In strategic games, we define risk attitude and reputation, which are factors that decision-makers take into account in making decisions. We transform a strategic game to a risk game. We propose a new kind of strategies, called risk strategies. In the transformed risk game, we find a new kind of equilibrium, called risk strategy equilibrium. We also find out some properties of risk strategy equilibrium. In addition, we find that players can obtain higher payoffs in risk strategy equilibrium than in pure strategy Nash equilibrium. / One of the key properties defining an intelligent agent is social ability. This means that an intelligent agent should be able to interact with other agents or humans. Before designing an intelligent agent for any multi-agent system, we need to first understand how agents should behave and interact in that particular application. / One way to understand how agents should behave in a particular application is to model the application as a game. Besides, many real-life situations can be modeled as games. So, we extend the model of attractiveness maximization and apply the extended model to strategic games and infinitely repeated games. / The reason why most of the people do not maximize the expected utility is that people have different attitudes towards risk in different situations and people are generally risk-averse. To model this human behavior, we propose another way of decision-making, called attractiveness maximization. In this model, every choice has an attractiveness, which is calculated from the risk attitude of the decision-maker, probability, and utility. In making decisions, decision-makers choose the choice with the maximum attractiveness. Using attractiveness maximization, the phenomenon that human do not maximize expected utility can be explained. We also find some properties of the model of attractiveness maximization, which match the human behaviors. / We develop several applications of attractiveness maximization and risk strategies. First, we apply the proposed concepts to the Iterated Prisoner's Dilemma, which is widely used by economists and sociologists to model and simulate many of the human interactions. Simulation shows that agents have improved performance and are reactive as well as pro-active. Second, we construct behavioral predictors and an adaptive strategy for Minority Games, which model many real life situations like the financial market, auctions and resources competitions. Simulations show that the adaptive strategy works much better than previous models. Third, we model a resource allocation problem as a Minority Game and apply the behavioral predictors and the adaptive strategy to the resource allocation problem. Simulations also show that agents with the proposed adaptive strategy are able to make more right decisions and better resource utilization than previous work. / Lam, Ka Man. / "August 2007." / Adviser: Leung Ho Fung. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1107. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 159-173). / 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. / Abstract in English and Chinese. / School code: 1307.

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.

Wang, Yang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 72-74). / Abstracts in English and Chinese. / Chapter 1 --- Literature Review and Model Description --- p.1 / Chapter 1.1 --- Portfolio theory under mean-variance framework --- p.2 / Chapter 1.2 --- Portfolio theory under utility-maximizing framework --- p.5 / Chapter 1.3 --- Model Description --- p.11 / Chapter 2 --- Parameterized optimal rebalancing strategy --- p.14 / Chapter 2.1 --- An open-loop policy of the T-horizon model --- p.16 / Chapter 2.2 --- A closed-loop policy of the T-horizon model --- p.24 / Chapter 2.3 --- Illustrative numerical example --- p.36 / Chapter 3 --- Non-parameterized optimal rebalancing model --- p.46 / Chapter 3.1 --- T=2 period problem --- p.47 / Chapter 3.2 --- T=3 period problem --- p.55 / Chapter 4 --- s-S type policy --- p.59 / Chapter 4.1 --- Exponential K-convex function --- p.60 / Chapter 4.2 --- Revised multiperiod portfolio selection model --- p.62 / Chapter 5 --- Conclusion and summary of work --- p.70 / Bibliography --- p.71

Fu, Hoi Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 31-34). / Abstract also in Chinese.

Cheung, Kwan Hung Edwin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 39-40). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Levy Process --- p.4 / Chapter 2.1 --- Levy-Khintchine representation --- p.5 / Chapter 2.2 --- Variance Gamma process --- p.6 / Chapter 3 --- Minimum-Variance Static Hedge with Index futures --- p.8 / Chapter 3.1 --- Capital Asset Pricing Model with static hedge --- p.10 / Chapter 3.2 --- Continuous CAPM under Levy process --- p.11 / Chapter 4 --- Option pricing under Levy process --- p.15 / Chapter 4.1 --- Option pricing under the fast Fourier transform --- p.16 / Chapter 4.2 --- The modified fast Fourier transform on call option price --- p.19 / Chapter 5 --- Empirical Results --- p.23 / Chapter 5.1 --- Proposed model for empirical studies --- p.25 / Chapter 5.2 --- Calibration Procedure and Estimates of Betas --- p.26 / Chapter 5.3 --- Hedging performance of Betas --- p.32 / Chapter 6 --- Conclusion --- p.37 / Bibliography --- p.39

Ng, Hon Yip. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 79-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Basic Concepts in Portfolio Theory --- p.8 / Chapter 2.1 --- Statistical Model --- p.8 / Chapter 2.2 --- Mean-Variance Optimization --- p.9 / Chapter 2.3 --- The Efficient Frontier --- p.11 / Chapter 2.4 --- The Tangency Portfolio and The Capital Market Line --- p.13 / Chapter 2.5 --- Mathematical Formulation of Portfolio Optimization --- p.17 / Chapter 3 --- Derivation of The Improved Estimator --- p.29 / Chapter 4 --- Simulation Study --- p.40 / Chapter 4.1 --- Procedure of Simulation --- p.40 / Chapter 4.2 --- Simulation Results --- p.46 / Chapter 4.2.1 --- Zero Correlation --- p.47 / Chapter 4.2.2 --- Positive Correlations --- p.50 / Chapter 4.2.3 --- Negative Correlations --- p.52 / Chapter 5 --- Conclusion and Future Direction --- p.56 / Chapter A --- Simulation results for p = 200 --- p.58 / Chapter B --- Simulation results for p = 400 --- p.61 / Chapter C --- Simulation results for p = 500 --- p.64 / Chapter D --- Simulation results for p = 200 with negative correlations --- p.67 / Chapter E --- Simulation results for p = 400 with negative correlations --- p.71 / Chapter F --- Simulation results for p = 500 with negative correlations --- p.75 / Bibliography --- p.79