University of Macau / Faculty of Science and Technology / Department of Mathematics

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Thesis (Ph.D.)--University of Florida, 2005. / Title from title page of source document. Document formatted into pages; contains 158 pages. Includes vita. Includes bibliographical references.

A thesis submitted for the degree of Doctor of Philosophy 2013 / This thesis presents a range of related pricing kernel models that are driven by incomplete information about a series of future unknowns. These unknowns may, for instance, represent fundamental macroeconomic, political or social random variables that are revealed at future times. They may also represent latent or hidden factors that are revealed asymptotically. We adopt the information-based approach of Brody, Hughston and Macrina (BHM) to model the information processes associated with the random variables. The market filtration is generated collectively by these information processes. By directly modelling the pricing kernel, we generate information-sensitive arbitrage-free models for the term structure of interest rates, the excess rate of return required by investors, and security prices. The pricing kernel is modelled by a supermartingale to ensure that nominal interest rates remain non-negative. To begin with, we primarily investigate finite-time pricing kernel models that are sensitive to Brownian bridge information. The BHM framework for the pricing of credit-risky instruments is extended to a stochastic interest rate setting. In addition, we construct recovery models, which take into consideration information about, for example, the state of the economy at the time of default. We examine various explicit examples of analytically tractable information-driven pricing kernel models. We develop a model that shares many of the features of the rational lognormal model, and investigate examples of heat kernel models. It is shown that these models may result in discount bonds and interest rates being bounded by deterministic functions. In certain situations, incoming information about random variables may exhibit jumps. To this end, we construct a more general class of nite-time pricing kernel models that are driven by Levy random bridges. Finally, we model the aggregate impact of uncertainties on a nancial market by randomised mixtures of Levy and Markov processes respectively. It is assumed that market participants have incomplete information about the underlying random mixture. We apply results from non-linear ltering theory and construct Flesaker-Hughston models and in nite-time heat kernel models based on these randomised mixtures.

The first essay considers a dynamic non-stationary inventory problem in which replenishment is made in fixed lot sizes (e.g., in full truckloads or full containers). We consider two separate cases: one with exogenous pricing and the other with endogenous pricing. In the first case (exogenous pricing), we show that when the ordering cost contains only a variable component, the reorder-point lot-size policy or (r, Q) policy is optimal for both single-stage and multi-echelon inventory systems. In the presence of a fixed cost, we establish the optimality of batch based (s, S ) policies for the single-stage inventory system. In the second case (endogenous pricing), we show that when the demand function has the additive form and there is only a variable ordering cost, the (r,Q) list-price policy is optimal for the single-stage system, where inventory replenishment follows an (r,Q) policy and the optimal price in each period depends on the order-up-to level. / The second essay analyzes a periodic-review, stochastic, inventory-control system in which the fixed order-cost is a step function of the order size. In particular, if the order size is within a specified limit, C, then the setup cost is K1; otherwise it is K2, where K2 ≥ K1. This cost structure is motivated from some industrial applications and transportation/production contracts used in practice. Under the condition that K1 ≤ K 2 ≤ K1, we introduce a new concept called C - (K1 ≤ K 2) convexity, which enables us to partially characterize the structure of an optimal ordering policy. For the general condition K 1 ≤ K2 , the analysis is facilitated with a different notion called strong K-convexity. Based on this analysis, we provide a partial characterization of the optimal policy and construct an easy-to-implement heuristic method that has near-optimal performance in random test instances. Our study extends or redevelops (with different techniques) several existing results in the literature. / The third essay studies a firm's periodic-review production/inventory ordering decisions when the next period's setup cost depends on the quantity produced/ ordered in the current period. In particular, if the current period's production/order quantity exceeds a specified threshold value, the system starts the next period in a "warm" state and no fixed setup cost is incurred; otherwise the state is considered "cold" and a positive setup cost is required for production/ ordering. We develop a dynamic programming formulation of the problem and provide a partial characterization of the optimal policy under the assumption that the demands follow a Polya or Uniform distribution. We use the structural results to develop fairly simple heuristic policies, which perform highly effectively in our computational experiments. / With increased globalization and competition in the current market, supply chain has become longer and more complicated than ever before. An effective and efficient supply chain is crucial and essential to a successful firm. In a supply chain, inventories are a very important component as the investment in inventories is enormous. This dissertation consists of three essays related to stochastic inventory management. / Yang, Yi. / Adviser: Youhua Chen. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 145-151). / 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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] 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.

by Chen Xi. / "July 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 107-112). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Zhang Li. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 67-69). / Abstracts in English and Chinese. / Chapter 1 --- Introduction and Literature Review --- p.1 / Chapter 2 --- The Tracking Portfolio Models --- p.7 / Chapter 2.1 --- Problem Formulation --- p.8 / Chapter 2.2 --- Reformulation of Tracking Models --- p.12 / Chapter 2.3 --- A Stochastic LQ Control Approach --- p.13 / Chapter 3 --- Efficient Tracking: Deterministic Market Parameters --- p.16 / Chapter 3.1 --- Solution to Model I --- p.17 / Chapter 3.2 --- A Special Case of Model I --- p.23 / Chapter 3.3 --- Solution to Model II --- p.24 / Chapter 3.4 --- A Special Case of Model II: Mean-Variance Portfolio Selection --- p.32 / Chapter 3.5 --- Solution to Model III --- p.36 / Chapter 4 --- Efficient Tracking: Markov-Modulated Market Parameters --- p.41 / Chapter 4.1 --- Problem Formulation --- p.42 / Chapter 4.2 --- Solution to Model I with Regime Switching --- p.47 / Chapter 4.3 --- Solution to Model II with Regime Switching --- p.52 / Chapter 4.4 --- Solution to Model III with Regime Switching --- p.59 / Chapter 5 --- Conclusion --- p.64 / Bibliography --- p.66

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Univ., Diss.--Bremen, 2002.

Thesis (M. S.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Reveliotis, Spyros; Committee Member: Ayhan, Hayriye; Committee Member: Goldsman, Dave; Committee Member: Shamma, Jeff; Committee Member: Zwart, Bert.