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.

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.

Key Words: continuous-time model, mean-variance, transaction costs, stochastic singular control, Lagrange multiplier method, parabolic free-boundary problem, double-obstacle problem, Skorokhod problem. / We study continuous-time Markowitz's mean-variance portfolio selection problem in a market with one stock, one bond and proportional transaction costs. The presence of transaction costs makes the problem being a singular control problem in a finite time horizon, which is very hard to deal with from the point view of control theory. Using a partial differential equation approach, we formulate the problem as a double obstacle problem, and prove the smoothness of the value function. Then we give the necessary and sufficient conditions for the existence of an optimal solution and completely characterize the optimal strategy when the problem is feasible. We show three critical distinctive features of the Markowitz model under the presence of transaction costs. First, the expected return on the portfolio could be too high to achieve if the time to maturity is not long enough, while without transaction costs, any expected return can be reached in an arbitrary short time. Second, instead of keeping the investment ratio between stock and bond to be a constant, there exists time-dependent upper and lower boundaries, transaction is carried out only if the investment ratio is on the boundaries. Third, there exists a critical time, which only depends on the market parameters, such that beyond the time no more investment will be added to stock holding. Our result is closer to real investment practice where people tend not to invest on risky assets towards the end of the investment horizon. / Xu Zuoquan. / "January 2007." / Adviser: Xunyu Zhou. / Source: Dissertation Abstracts International, Volume: 68-08, Section: B, page: 5290. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 118-123). / 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. / Abstracts in English and Chinese. / School code: 1307.

Kam, Kwok Hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 100-103). / Abstracts in English and Chinese. / Abstract Page --- p.11 / Abstract (Chinese) --- p.12 / Acknowledgment Page --- p.13 / Table of Contents --- p.1 / Table of Figures --- p.1 / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Utility and Value Function --- p.5 / Chapter 1.2.1 --- Expected utility theory --- p.5 / Chapter 1.2.2 --- Prospect Theory --- p.9 / Chapter 1.3 --- Mental Accounting --- p.14 / Chapter 1.3.1 --- Segregation vs Aggregation --- p.17 / Chapter 2 --- Moving reference point with loss aversion --- p.21 / Chapter 2.1 --- Model Setup --- p.21 / Chapter 2.2 --- Simulation Results --- p.27 / Chapter 3 --- Constant Rebalancing Portfolio with Additive Utility --- p.30 / Chapter 3.1 --- Model setting --- p.31 / Chapter 3.1.1 --- Additive Utility Theory (AUT) --- p.33 / Chapter 3.2 --- Analysis --- p.34 / Chapter 3.3 --- Results --- p.35 / Chapter 3.4 --- Summary --- p.38 / Chapter 4 --- Revision of Gomes´ة Work --- p.40 / Chapter 4.1 --- Background --- p.40 / Chapter 4.2 --- Portfolio Allocation with zero surplus wealth --- p.44 / Chapter 4.3 --- Portfolio Allocation with Negative Surplus --- p.46 / Chapter 4.4 --- Portfolio Allocation with Positive Surplus --- p.50 / Chapter 4.5 --- Numerical Results --- p.51 / Chapter 4.5.1 --- Gomes´ة Work --- p.56 / Chapter 4.6 --- Summary --- p.57 / Chapter 5 --- Mental Accounting under Value Function in the Prospect Theory --- p.59 / Chapter 5.1 --- Cognitive dissonance --- p.59 / Chapter 5.2 --- Market Setting --- p.60 / Chapter 5.3 --- Single Mental Account --- p.61 / Chapter 5.4 --- Two Mental Accounts --- p.63 / Chapter 5.5 --- Numerical results --- p.67 / Chapter 5.5.1 --- Pessimistic View --- p.71 / Chapter 5.6 --- Summary --- p.72 / Chapter 6 --- Mental Accounting under Friedman-Savage Value Function --- p.74 / Chapter 6.1 --- Two Assets with Single mental account --- p.76 / Chapter 6.1.1 --- Different Sharpe ratios --- p.78 / Chapter 6.1.2 --- Same Sharpe ratio --- p.82 / Chapter 6.2 --- Two Assets with two mental accounts --- p.85 / Chapter 6.2.1 --- Segregation or Aggregation --- p.86 / Chapter 6.2.2 --- Numerical results --- p.90 / Chapter 6.3 --- Summary --- p.93 / Chapter 7 --- Conclusion --- p.96 / Bibliography --- p.100

Jiang, Kening. / "August 2011." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 90-93). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Portfolio Selection Using Clustering Methodology --- p.7 / Chapter 2.1 --- Heuristic algorithm --- p.8 / Chapter 2.1.1 --- Step 1: Security transformation by factor model --- p.8 / Chapter 2.1.2 --- Step 2: Clustering algorithm --- p.10 / Chapter 2.1.3 --- Step 3: Representative selection by t he Sliarpe ratio --- p.16 / Chapter 2.2 --- Numerical results --- p.17 / Chapter 3 --- Modified Portfolio Selection Using Clustering Methodology --- p.22 / Chapter 3.1 --- Analysis of artificial factors --- p.23 / Chapter 3.2 --- Problem reformulation --- p.27 / Chapter 3.3 --- Numerical results --- p.29 / Chapter 4 --- Minimum Variance Point --- p.70 / Chapter 4.1 --- Iterative elimination scheme I --- p.72 / Chapter 4.2 --- Iterative elimination scheme II --- p.74 / Chapter 4.3 --- Orthogonal matrix mapping --- p.76 / Chapter 4.4 --- Condition to solve diagonal dominant problem --- p.77 / Chapter 4.5 --- L1 formulation --- p.82 / Chapter 4.6 --- Numerical results --- p.85 / Chapter 5 --- Summary and Future work --- p.88

This study examines the performance of recently introduced passively-managed exchange-traded hedged funds (HETFs). Using data that cover the period 2008 to 2017 of all available HETFs under global macro and long-short classifications with sufficient number of observations, the study provides the most complete and update measure and documentation of the performance of these two fund categories. Little research has been done on HETFs' performance in despite of the rapid growth and expected future expansion of their market sizes, since the introduction of HETFs expands for ordinary investors investment opportunity set that were only available to high net wealth individuals and institutions. Using a simple 3-three factor model including equity, bond and volatility factors, it shows long-short HETFs cannot closely follow the returns of their corresponding indexes as global macro HETFs. By using Fung and Hsieh's (2004) 7-factor model, and Edelman, Fung and Hsieh's (2012) revised 8-factor model, significant negative alphas are found for strategy portfolios. The relatively poor performance of the HETFs can be attributed to their high expense ratio and their failure to closely track the benchmark index.

This dissertation consist of three contributions to financial and insurance mathematics. The first part considers numerical methods for dynamic portfolio optimisation in the expected utility model. The aim is to compare the risk-neutral computational approach (RNCA) also known as the martingale approach to stochastic dynamic programming (SDP) in a discrete-time setting. The main idea of the RNCA is to use the completeness and the arbitrage free properties of the market to compute the optimal consumption rules and then determine the trading strategy that finance this optimal consumption. In contrast, SDP solves for the optimal consumption and investment rules simultaneously using backward recursion and the principle of optimality. The setting that we consider is a discrete time and state space lattice. We provide some new theoretical results relating to the Hyperbolic Absolute Risk Aversion class of utility functions as well as propose a straightforward implementation of RNCA in binomial and trinomial lattices. Moreover, instead of discretizing the Hamilton-Jacobi-Bellman equation with possibly more than one state variable, we use symbolic algorithms to implement stochastic dynamic programming. This new approach provides a simpler numerical procedure for computing optimal consumption-investment policies. A comparison of the RNCA with SDP demonstrates the superiority of the RNCA in terms of computation. The second part considers the pricing of contingent claims using an approach developed and applied in applied in insurance. This approach utilize probability distortion functions as the dual of the utility functions used in financial theory. The main idea of the dual theory is to distort the subjective probabilities rather than outcomes to express the investor????????s risk aversion. In the first part, the RNCA for asset allocation uses the same principle as risk-neutral valuation for derivative pricing. The idea of the second part of this research is to show that the risk-neutral valuation can be recovered from the probability distortion function approach, thereby establishing consistency between the insurance and the financial approaches. We prove that pricing contingent claims under the real world probability measure using an appropriate distortion operator produces arbitrage-free prices when the underlying asset prices are log-normal. We investigate cases when the insurance-based approach fails to produce arbitrage-free prices and determine the appropriate distortion operator under more general assumptions than those used in Black-Scholes option pricing. In the third part we introduce dynamic portfolio optimisation with risk measures based on probability distortion function and provide a formal treatment of this class of risk measures. We employ the RNCA to study the consumption-investment problem in discrete time with preferences consistent with Yaari????????s dual (non-expected utility) theory of choice. As an application, we first consider risk measures based on the Proportional Hazard Transform that treats the upside and downside of the risk differently and secondly a risk measure based on the standard Normal cumulative distribution function. When the objective is to maximise a dual utility of wealth, and the underlying security returns are normal, the efficient frontier is found to be the same as in the mean-variance portfolio problem for an equivalent risk tolerance. When the objective is to maximise a dual utility of consumption, then ????????plunging???????????? behaviour occurs ( investing everything is the risky asset). Other properties of the optimal consumption-investment policies in the dual theory are also investigated and discussed.

Thesis (Ph. D.)--University of Texas at Austin, 1999 / Vita Includes bibliographical references (p. 202-206)

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 88-99).