by Chi-van Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 71-72). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- The Model and the Bayes risk --- p.7 / Chapter § 2.1 --- The Model / Chapter § 2.2 --- The Bayes risk / Chapter Chapter 3 --- The Algorithm --- p.16 / Chapter § 3.1 --- A finite algorithm / Chapter § 3.2 --- The Number Theoretical Method for Optimization / Chapter § 3.2.1 --- NTMO / Chapter § 3.2.2 --- SNTMO / Chapter Chapter 4 --- Quadratic Loss Function --- p.26 / Chapter §4.1 --- The Bayes risk / Chapter § 4.2 --- An optimal plan / Chapter § 4.3 --- Numerical Examples / Chapter Chapter 5 --- Conclusions and Comments --- p.42 / Chapter § 5.1 --- Comparison between various plans / Chapter § 5.2 --- Sensitivity Analysis / Chapter § 5.3 --- Further Developments / Tables --- p.46 / Appendix A --- p.60 / Appendix B --- p.65 / References --- p.71

This thesis describes the Delta-Normal method of computing Value-at-Risk. The advantages and disadvantages of the Delta-Normal method compared to the Historical and Monte Carlo method of computing Value-at-Risk are discussed. The Delta-Normal method of computing Value-at-Risk is compared with the Historical Simulation method of Value-at-Risk using an implementation of portfolio consisting of ten stocks for 400 time intervals. Based on the normality of the distribution of the portfolio risk factors, Delta-Normal would be suitable if the distribution is normal and Historical Simulation method of calculating Value-at-Risk would be ideally suited if the distribution is non-normal.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 364-373. / by Robert Buchanan Washburn, Jr. / Ph.D.

The first part of this thesis considers the residual empirical process of a nearly unstable long-memory time series. Chan and Ling [8] showed that the usual limit distribution of the Kolmogorov-Smirnov test statistics does not hold when the characteristic polynomial of the unstable autoregressive model has a unit root. A key question of interest is what happens when this model has a near unit root, that is, when it is nearly non-stationary. In this thesis, it is established that the statistics proposed by Chan and Ling can be extended. The limit distribution is expressed as a functional of an Orenstein-Uhlenbeck process that is driven by a fractional Brownian motion. This result extends and generalizes Chan and Ling's results to a nearly non-stationary long-memory time series. / The second part of the thesis investigates the weak convergence of weighted sums of random variables that are functionals of moving aver- age processes. A non-central limit theorem is established in which the Wiener integrals with respect to the Hermite processes appear as the limit. As an application of the non-central limit theorem, we examine the asymptotic theory of least squares estimators (LSE) for a nearly unstable AR(1) model when the innovation sequences are functionals of moving average processes. It is shown that the limit distribution of the LSE appears as functionals of the Ornstein-Uhlenbeck processes driven by Hermite processes. / Liu, Weiwei. / Adviser: Chan Ngai Hang. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 60-67). / 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. / Abstract also in Chinese.

This dissertation is motivated by the problem of uncertainty and sensitivity in business- class models such as the carbon emission abatement policy model featured in this work. Uncertain model inputs are represented by numerical random variables and a computational methodology is developed to numerically compute business-class models as if sharp inputs were given. A new description for correlation of random variables is presented that arises spontaneously within a numerical model. Methods of numerically computing correlated random variables are implemented in software and represented. The major contribution of this work is a methodology for the numerical computation of models under uncertainty that expresses no preference for unlikelihood of model input combinations. The methodology presented here serves a sharp contrast to traditional Monte Carlo methods that implicitly equate likelihood of model input values with importance of results. The new methodology herein shifts the computational burden from likelihood of inputs to resolution of input space.

by A. S. Willsky, N. R. Sandell. / Grants AFOSR-77-3281B and ONR-N00014-76-C-0346. / Bibliography: leaf 34.

Thesis (M. Phil.)--University of Hong Kong, 2009. / Includes bibliographical references (leaves 82-87). Also available in print.

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