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

Lam, Ho Man. / "August 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 42-43). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Levy Process --- p.5 / Chapter 2.1 --- Merton's Jump-Diffusion model (1976) --- p.8 / Chapter 2.2 --- Estimation of Levy processes --- p.9 / Chapter 3 --- Transform Martingale Estimation --- p.11 / Chapter 3.1 --- Maximum Likelihood Estimation --- p.11 / Chapter 3.2 --- Transform Martingale Estimating Functions --- p.13 / Chapter 3.2.1 --- Transform Quasi-Score Function --- p.15 / Chapter 3.2.2 --- Composite Quasi-Score Function --- p.17 / Chapter 3.2.3 --- Implementation Issue --- p.18 / Chapter 3.2.4 --- Transform Martingale Estimation on Levy process --- p.21 / Chapter 4 --- Structural Models of Credit Risk --- p.22 / Chapter 4.1 --- Overview --- p.22 / Chapter 4.2 --- Merton's structural credit risk model (1974) --- p.23 / Chapter 4.3 --- Estimation Methodologies --- p.24 / Chapter 4.4 --- Martingale Estimation with KMV's Method --- p.26 / Chapter 5 --- Simulation Study --- p.28 / Chapter 5.1 --- Equity Estimation --- p.28 / Chapter 5.2 --- Estimation of Structural Models --- p.37 / Chapter 6 --- Conclusion --- p.41 / Bibliography --- p.42

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

Liu, Weiyang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 111-113). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction and Literature Review --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- Background and Motivating examples --- p.2 / Chapter 1.1.2 --- Basic Concepts --- p.4 / Chapter 1.1.3 --- Outline of the thesis --- p.6 / Chapter 1.2 --- Literature Review --- p.8 / Chapter 2 --- Multi-period Cooperative Re-investment Games: The Basic Model --- p.11 / Chapter 2.1 --- Basic settings and assumptions --- p.11 / Chapter 2.2 --- The problem --- p.13 / Chapter 3 --- Three sub-models and the allocation rule of Sub-Model III --- p.17 / Chapter 3.1 --- Three possible sub-models of the basic model --- p.17 / Chapter 3.1.1 --- Sub-model I --- p.17 / Chapter 3.1.2 --- Sub-model II --- p.18 / Chapter 3.1.3 --- Sub-model III --- p.19 / Chapter 3.2 --- The allocation rule of Sub-model III --- p.19 / Chapter 4 --- A two period example of the revised basic model --- p.25 / Chapter 4.1 --- The two period example with two projects --- p.25 / Chapter 4.2 --- The algorithm for the dual problem --- p.29 / Chapter 5 --- Extensions of the Basic Model --- p.35 / Chapter 5.1 --- The model with stochastic budgets --- p.36 / Chapter 5.2 --- The core of the model with stochastic budgets --- p.39 / Chapter 5.3 --- An example: the two-period case of models with stochastic bud- gets and an algorithm for the dual problem --- p.46 / Chapter 5.4 --- An interesting marginal effect --- p.52 / Chapter 5.5 --- "A Model with stochastic project prices, stochastic returns and stochastic budgets" --- p.54 / Chapter 6 --- Multi-period Re-investment Model with risks --- p.58 / Chapter 6.1 --- The Model with l1 risk measure --- p.58 / Chapter 6.2 --- The Model with risk measure --- p.66 / Chapter 7 --- Numerical Tests --- p.70 / Chapter 7.1 --- The affects from uncertainty changes --- p.71 / Chapter 7.2 --- The affects from budget changes --- p.71 / Chapter 7.3 --- The affects from the budget changes of only one group --- p.71 / Chapter 8 --- Conclusive Remarks --- p.77 / Chapter A --- Original Data and Analysis for Section 7.1 (Partial) --- p.79 / Chapter B --- Data Analysis for Section 7.2 (Partial) --- p.95 / Chapter C --- Data Analysis for Section 7.3 (Partial) --- p.98

Zhou, Ying. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 89-91). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Aims and objectives --- p.2 / Chapter 1.3 --- Outline of the thesis --- p.3 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- Portfolio Optimization Problems --- p.6 / Chapter 2.2 --- Cooperative Games and Cooperative Investment Models --- p.8 / Chapter 2.2.1 --- Linear Production Games And Basic Concepts of Co- operative Game Theory --- p.9 / Chapter 2.2.2 --- Investment Models Using Linear Production Games --- p.12 / Chapter 3 --- Multi-period Cooperative Investment Games: Basic Model --- p.15 / Chapter 3.1 --- Cooperative Investment Game under Deterministic Case --- p.16 / Chapter 3.2 --- Cooperative Investment Game with Stochastic Return --- p.18 / Chapter 3.2.1 --- Basic Assumptions --- p.18 / Chapter 3.2.2 --- Choose the Proper Risk Measure --- p.20 / Chapter 3.2.3 --- One Period Case --- p.21 / Chapter 3.2.4 --- Multi-Period Case --- p.23 / Chapter 4 --- The Two-Period Investment Game under L∞ Risk Measure --- p.26 / Chapter 4.1 --- The Two Period Model --- p.26 / Chapter 4.2 --- The Algorithm --- p.35 / Chapter 4.3 --- Optimal Solution of the Dual --- p.41 / Chapter 5 --- Primal Solution and Stability of the Core under Two-Period Case --- p.43 / Chapter 5.1 --- Direct Results --- p.44 / Chapter 5.2 --- Find the Optimal Solutions of the Primal Problem --- p.46 / Chapter 5.3 --- Relationship between A and the Core --- p.53 / Chapter 5.3.1 --- Tracing out the efficient frontier --- p.54 / Chapter 6 --- Multi-Period Case --- p.63 / Chapter 6.1 --- Common Risk Price and the Negotiation Process with Concave Risk Utility --- p.64 / Chapter 6.1.1 --- Existence of Common Risk Price and Core --- p.65 / Chapter 6.1.2 --- Negotiation Process --- p.68 / Chapter 6.2 --- Modified Simplex Method --- p.71 / Chapter 7 --- Other Risk Measures --- p.76 / Chapter 7.1 --- The Downside Risk Measure --- p.76 / Chapter 7.1.1 --- Discrete (Finite Scenario) Distributions --- p.78 / Chapter 7.1.2 --- General Distributions --- p.81 / Chapter 7.2 --- Coherent Risk Measure and CVaR --- p.83 / Chapter 8 --- Conclusion and Future Work --- p.87

In recent years, the Markov Regime-Switching model and the class of Archimedean copulas have been widely applied to a variety of finance-related fields. The Markov Regime-Switching model can reflect the reality that the underlying economy is changing over time. Archimedean copulas are one of the most popular classes of copulas because they have closed form expressions and have great flexibility in modeling different kinds of dependencies. In the thesis, we first consider a discrete-time risk process based on the compound binomial model with regime-switching. Some general recursive formulas of the expected penalty function have been obtained. The orderings of ruin probabilities are investigated. In particular, we show that if there exists a stochastic dominance relationship between random claims at different regimes, then we can order ruin probabilities under different initial regimes. Regarding capital allocation problems, which are important areas in finance and risk management, this thesis studies the problems of optimal allocation of policy limits and deductibles when the dependence structure among risks is modeled by an Archimedean copula. By employing the concept of arrangement increasing and stochastic dominance, useful qualitative results of the optimal allocations are obtained. Then we turn our attention to a new family of risk measures satisfying a set of proposed axioms, which includes the class of distortion risk measures with concave distortion functions. By minimizing the new risk measures, we consider the optimal allocation of policy limits and deductibles problems based on the assumption that for each risk there exists an indicator random variable which determines whether the risk occurs or not. Several sufficient conditions to order the optimal allocations are obtained using tools in stochastic dominance theory. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

In this thesis, efforts are devoted to the stochastic modeling, measurement and evaluation of credit risks, the development of mathematical and statistical tools to estimate and predict these risks, and methods for solving the significant computational problems arising in this context. The reduced-form intensity based credit risk models are studied. A new type of reduced-form intensity-based model is introduced, which can incorporate the impacts of both observable trigger events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with trigger events. In addition, this thesis focuses on the relationship between structural firm value model and reduced-form intensity based model. A continuous time structural asset value model for the asset value of two correlated firms with a two-dimensional Brownian motion is studied. With the incomplete information introduced, the information set available to the market participants includes the default time of each firm and the periodic asset value reports. The original structural model is first transformed into a reduced-form model. Then the conditional distribution of the default time as well as the asset value of each name are derived. The existence of the intensity processes of default times is proven and explicit form of intensity processes is given in this thesis. Discrete-time Markovian models in credit crisis are considered. Markovian models are proposed to capture the default correlation in a multi-sector economy. The main idea is to describe the infection (defaults) in various sectors by using an epidemic model. Green’s model, an epidemic model, is applied to characterize the infectious effect in each sector and dependence structures among various sectors are also proposed. The models are then applied to the computation of Crisis Value-at-Risk (CVaR) and Crisis Expected Shortfall (CES). The relationship between correlated defaults of different industrial sectors and business cycles as well as the impacts of business cycles on modeling and predicting correlated defaults is investigated using the Probabilistic Boolean Network (PBN). The idea is to model the credit default process by a PBN and the network structure can be inferred by using Markov chain theory and real-world data. A reduced-form model for economic and recorded default times is proposed and the probability distributions of these two default times are derived. The numerical study on the difference between these two shows that our proposed model can both capture the features and fit the empirical data. A simple and efficient method, based on the ordered default rate, is derived to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. Analytical expressions for the ordered default time distributions with recursive formulas for the coefficients are given, which makes the calculation fast and efficient in finding rates of basket CDSs. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

This dissertation describes two theories of risky choice based on a normatively axiomatized partial order. The first theory is an atemporal alternative to von Neumann and Morgenstern's Expected Utility Theory that accommodates the status quo bias, violations of Independence and preference reversals. The second theory is an extension of the Inter-temporal von Neumann-Morgenstern theory of Kreps and Porteus (1978) that features a normatively deduced preference for flexibility. A substantial part of the thesis is devoted to examining equilibrium implications of the inter-temporal theory. In particular, a multi-agent multi-period Bayesian rational expectations equilibrium is shown to exist under certain conditions. Implications to asset pricing are then investigated with an explicit parameterization of the model.

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We propose a systematic framework for designing adaptive trading strategies that minimize both the mean and the variance of the execution costs. This is achieved by diversifying risk over sequential decisions in discrete time. By incorporating previous trading performance as a state variable, the framework can dynamically adjust the risk-aversion level for future trading. This incorporation also allows the framework to solve the mean-variance problems for different risk aversion factors all at once. After developing this framework, it is then applied to solve three algorithmic trading problems. The first two are trade scheduling problems, which address how to split a large order into sequential small orders in order to best approximate a target price – in our case, either the arrival price, or the Volume-Weighed-Average-Price (VWAP). The third problem is one of optimal execution of the resulting small orders by submitting market and limit orders. Unlike the tradition in both academia and industry of treating the scheduling and order placement problems separately, our approach treats them together and solves them simultaneously. In out-of-sample tests, this unified strategy consistently outperforms strategies that treat the two problems separately.