Wan Po Man Polly. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 122-128). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgements --- p.v / Contents --- p.vi / List of Figures --- p.x / List of Tables --- p.xiv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation and Aims --- p.1 / Chapter 1.2 --- Organization of Thesis --- p.5 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- Dimensionality Reduction --- p.6 / Chapter 2.1.1 --- Fourier Transformation --- p.6 / Chapter 2.1.2 --- Wavelet Transformation --- p.8 / Chapter 2.1.3 --- Singular Value Decomposition --- p.10 / Chapter 2.2 --- Searching Sequence Similarity with Transformation --- p.11 / Chapter 2.2.1 --- Time Warping --- p.11 / Chapter 2.2.2 --- Amplitude Scaling and Shifting --- p.14 / Chapter 2.3 --- Data Smoothing and Noise Removal --- p.18 / Chapter 2.3.1 --- Piecewise Linear Segmentations --- p.18 / Chapter 2.3.2 --- Approximation Function --- p.21 / Chapter 2.3.3 --- Best-fitting Line --- p.23 / Chapter 2.3.4 --- Turning Points --- p.24 / Chapter 3 --- Time-Series Searching with Scaling and Shifting in Amplitude and Time Domains --- p.25 / Chapter 3.1 --- Representation --- p.25 / Chapter 3.1.1 --- Control Points --- p.26 / Chapter 3.1.2 --- Lattice Structure --- p.28 / Chapter 3.1.3 --- Algorithm on Lattice Construction --- p.31 / Chapter 3.2 --- Pattern Matching --- p.32 / Chapter 3.2.1 --- Formulating the Problem of Similarity --- p.35 / Chapter 3.2.2 --- Error Measurement --- p.38 / Chapter 3.3 --- Indexing Scheme --- p.39 / Chapter 3.3.1 --- Indexing with scaling and shifting proposed by Chu and Wong --- p.40 / Chapter 3.3.2 --- Integrating with lattice structure --- p.41 / Chapter 3.4 --- Results --- p.43 / Chapter 4 --- Chart Patterns Searching for Chart Analysis --- p.47 / Chapter 4.1 --- Chart Patterns Overview --- p.47 / Chapter 4.1.1 --- Reversal Patterns --- p.49 / Chapter 4.1.2 --- Continuation Patterns --- p.52 / Chapter 4.2 --- Representation --- p.53 / Chapter 4.2.1 --- Trendline Preparation --- p.54 / Chapter 4.2.2 --- Trendline Pair --- p.59 / Chapter 4.3 --- Three-Phase Pattern Classification --- p.66 / Chapter 4.3.1 --- Phase One: Trendline Pair Classification --- p.66 / Chapter 4.3.2 --- Phase Two: Patterns Merging and Rejection --- p.74 / Chapter 4.3.3 --- Phase Three: Patterns Merging of Unclassified and Un- merged Trendline Pairs --- p.89 / Chapter 4.4 --- Results --- p.90 / Chapter 5 --- Conclusion --- p.100 / Chapter A --- Supplementary Results --- p.103 / Chapter A.1 --- Ascending Triangle --- p.103 / Chapter A.2 --- Descending Triangle --- p.104 / Chapter A.3 --- Falling Wedge --- p.106 / Chapter A.4 --- Head and Shoulders --- p.107 / Chapter A.5 --- Price Channel --- p.109 / Chapter A.6 --- Rectangle --- p.110 / Chapter A.7 --- Rising Wedge --- p.112 / Chapter A.8 --- Symmetric Triangle --- p.113 / Chapter A.9 --- Double Bottom --- p.113 / Chapter A.10 --- Double Top --- p.116 / Chapter A.11 --- Triple Bottom --- p.118 / Chapter A.12 --- Triple Top --- p.120 / Bibliography --- p.122 / Publications --- p.128

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 work contributes to the methodology of valuation of financial derivative contracts in an incomplete market. It focuses on a special type of incompleteness caused by the presence of a non-traded stochastic risk factor, affecting the value of the contract. The non-traded risk factor may only appear in the payoff of the contract or, in addition, may enter the dynamics of the traded asset. We consider both cases. We suggest a discrete time discrete space binomial model for the traded stock and the non-traded risk factor. We work in the utility maximization framework with dynamically changing agent's preferences. We present a discrete time multi-period analog of the forward and backward utility processes recently developed in continuous time. We use methods of stochastic control and provide the indifference valuation algorithm with both the forward and backward dynamic utilities. We compare the two approaches and provide conditions under which they assign the same value to the contract. We show that unlike the backward dynamic utility, the forward dynamic utility yields prices that do not depend on the end of the investment horizon. We pay attention to the choice of the equivalent martingale measure used for valuation (i.e., the minimal martingale measure and the minimal entropy measure for the forward and the backward utility processes correspondingly). We explicitly characterize both measures and give conditions under which they coincide. We extend our algorithm to the case of American and partial exercise contracts. We illustrate our work with numerical examples, showing that in an incomplete market, a call option on a non-traded risk factor may optimally be exercised early, and that it may be optimal to exercise only a fraction of the total number of contracts held, if partial exercise is allowed. In continuous time we extend the existing results to the case of American contracts with both the backward and the forward utilities. We emphasize the similarities between our discrete time valuation algorithm and the continuous time valuation. The two approaches use the same pricing measures, yield prices through nonlinear functionals of similar form, exhibit a similar relationship between the backward and forward prices, and a similar structure for the aggregate minimal entropy. We believe that our work makes a contribution by exposing the two above mentioned ways of dependence on the non-traded risk factor, and by providing a new dynamic indifference pricing algorithm that allows consistent valuation across different investment horizons.

For the last fifty years, the efficient market hypothesis has been the central pillar of economic thought and touted by all, despite Sanford Grossman’ and Nobel prize winner Joseph Stiglitz’ objection in 1980. Andrew Lo updated the efficient market hypothesis in 2004 to reconcile irrational human behavior and cold, calculating automatons. This thesis utilizes 33 years of oil futures, GARCH regressions, and the Jensen-Shannon informational criteria to provide extensive empirical objections to informational efficiency. The results demonstrate continuously inefficient oil future markets which exhibit decreased informational efficiency during recessionary periods, advocating the adaptive market hypothesis over the efficient market hypothesis. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

published_or_final_version / Statistics / Master / Master of Social Sciences