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Ph. D, Faculty of Science, University of Witwatersrand, 2011 / Research in the area of stochastic models for actuarial use in South Africa is limited to relatively few publications. Until recently, there has been little focus on actuarial stochastic models that describe the empirical stochastic behaviour of South African financial and economic variables. A notable exception is Thomson’s (1996) proposed methodology and model. This thesis presents a collection of five papers that were presented at conferences or submitted for peer review in the South African Actuarial Journal between 1996 and 2006. References to subsequent publications in the field are also provided. Such research has implications for medium and long-term financial simulations, capital adequacy, resilience reserving and asset allocation benchmarks as well as for the immunization of short-term interest rate risk, for investment policy determination and the general quantification and management of risk pertaining to those assets and liabilities. This thesis reviews Thomson’s model and methodology from both a statistical and economic perspective, and identifies various problems and limitations in that approach. New stochastic models for actuarial use in South Africa are proposed that improve the asset and liability modelling process and risk quantification. In particular, a new Multiple Markov-Switching (MMS) model framework is presented for modelling South African assets and liabilities, together with an optimal immunization framework for nominal liability cash flows. The MMS model is a descriptive model with structural features and parameter estimates based on historical data. However, it also incorporates theoretical aspects in its design, thereby providing a balance between purely theoretical models and those based only on empirical considerations.

This thesis presents results concerning the limiting behaviour of stochastic rumour processes. The first result involves our published analysis of the evolution for the general initial conditions of the (common) deterministic limiting version of the classical Daley-Kendall and Maki-Thompson stochastic rumour models, [14]. The second result being also part of the general analysis in [14] involves a new approach to stiflers in the rumour process. This approach aims at distinguishing two main types of stiflers. The analytical and stochastic numerical results of two types of stiflers in [14] are presented in this thesis. The third result is that the formulae to find the total number of transitions of a stochastic rumour process with a general case of the Daley-Kendall and Maki-Thompson classical models are developed and presented here, as already presented in [16]. The fourth result is that the problem is taken into account as an optimal control problem and an impulsive control element is introduced to minimize the number of final ignorants in the stochastic rumour process by repeating the process. Our published results are presented in this thesis as appeared in [15] and [86]. Numerical results produced by our algorithm developed for the extended [MT] model and [DK] model are demonstrated by tables in all details of numerical values in the appendices. / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2008

To reduce domestic military infrastructure, the United States enacted two laws that instituted rounds of base realignment and closure (BRAC) in 1988, 1991, 1993, and 1995. As a result of these BRAC rounds, the United States Army has closed or realigned 139 installations. Environmental cleanup is almost $2.3 billion (43%) of the entire cost associated with the closure and realignment of these 139 Army installations. The United States Army Base Realignment and Closure Office (BRACO) uses an integer linear program called BAEC (Budget Allocation for Environmental Cleanup) to help determine how to allocate limited yearly funding to installations for environmental cleanup. Considering environmental policies and yearly installation funding requests from 2002 to 2015, this thesis modifies BAEC to better account for uncertainty in future environmental cleanup cost estimates. Based on historic data that show most environmental cleanup cost estimates increase over time, the stochastic BAEC model recommends funding fewer sites than the deterministic BAEC model recommends. The stochastic BAEC model thereby provides funding recommendations with a better chance of staying within limited available yearly funding. / Turkish Army author

archives@tulane.edu / In this thesis, we examine models of scale invariant behavior in univariate, multivariate, and high-dimensional settings from the viewpoint of wavelet-based statistical inference, and construct a new class of models called operator fractional Lévy motion. The first part of this work pertains to tempered fractional Brownian motion (tfBm), a model that displays transient scale invariant behavior. We use wavelets to construct the first estimation procedure for tfBm as well as a simple and computationally efficient hypothesis test and study their properties. In the second part of this thesis, we construct a new class of non-Gaussian second-order scale invariance models called operator fractional Lévy motion (ofLm) and study its probabilistic behavior. We then study asymptotic properties of wavelet eigenanalysis estimation applied to ofLm and examine its performance. In the last portion of this work, we study the mathematical framework of wavelet eigenanalysis in a multivariate setting with a view towards high-dimensional scale invariance modeling. We then proceed to conduct wavelet-based eigenanalysis in a high-dimensional setting, and conclude with some computational experiments. / 1 / Benjamin Boniece

This thesis considers the possibility of stochastic resonance (SR) in the following nanoscale systems: (i) hard-threshold devices; (ii) averaging structures of carbon nanotubes (CNTs); (iii) myoglobin atoms; and finally (iv) tubulin dimers. The description of SR is carried out using Kramers' rate theory in the adiabatic two-state approximation for continuous systems and using Shannon's information theoretic formalism for systems with static nonlinearities. The effective potentials are modelled by asymmetric or symmetric bistable wells in a single reaction co-ordinate. Quantum considerations have not been invoked. Hence, all results are implicitly valid in the high-temperature regime of relevance to industrial applications. It is established that information transmitted by arrays of identical CNTs is maximized by non-zero noise intensities and that the response of myoglobin and tubulin dimers to ambient molecular forces (as described by the signal-to-noise ratio or SNR) is enhanced by increasing temperature. Sample calculations are shown for solvent fluctuations, ligand interactions and dipole oscillations. These results can be used to explain: (i) the effects of temperature observed in fabrication processes for CNTs; (ii) the dynamical transition observed in myoglobin and (iii) the 8.085 MHz resonance observed in microtubules.

This thesis considers the possibility of stochastic resonance (SR) in the following nanoscale systems: (i) hard-threshold devices; (ii) averaging structures of carbon nanotubes (CNTs); (iii) myoglobin atoms; and finally (iv) tubulin dimers. The description of SR is carried out using Kramers' rate theory in the adiabatic two-state approximation for continuous systems and using Shannon's information theoretic formalism for systems with static nonlinearities. The effective potentials are modelled by asymmetric or symmetric bistable wells in a single reaction co-ordinate. Quantum considerations have not been invoked. Hence, all results are implicitly valid in the high-temperature regime of relevance to industrial applications. It is established that information transmitted by arrays of identical CNTs is maximized by non-zero noise intensities and that the response of myoglobin and tubulin dimers to ambient molecular forces (as described by the signal-to-noise ratio or SNR) is enhanced by increasing temperature. Sample calculations are shown for solvent fluctuations, ligand interactions and dipole oscillations. These results can be used to explain: (i) the effects of temperature observed in fabrication processes for CNTs; (ii) the dynamical transition observed in myoglobin and (iii) the 8.085 MHz resonance observed in microtubules.

The present research formulates the path planning as an optimization problem with multiple objectives and stochastic edge parameters. The first section introduces different variants of the PP problem and discusses existing solutions to the problem. The next section introduces and solves various versions of the PP model within the scope of this research. The first three versions describe a single entity traveling from a single source to a single destination node. In the first version, the entity has a single objective and abides by multiple constraints. The second version deals with an entity traveling with multiple objectives and multiple constraints. The third version is a modification of the second version where the actual probability distributions of travel times along edges are known. The fourth and final version deals with multiple heterogeneous entities routed from multiple sources (supply nodes) to multiple destinations (demand nodes) along capacitated edges. Each of these formulations is solved by using either exact algorithms or heuristics developed in this research. The performance of each algorithm/heuristic is discussed in the final section. The main contributions of this research are: 1. Provide a framework for analyzing PP in presence of multiple objectives and stochastic edge parameters. 2. Identify candidate constraints where clustering based multi-level programming can be applied to eliminate infeasible edges. 3. Provide an exact O (V.E) algorithm for building redundant shortest paths. 4. Provide an O (V.E+C2) heuristic for generating Pareto optimal shortest paths in presence of multiple objectives where C is the upper bound for path length. The complexity can be further reduced to O (V.E) by using graphical read-out of the Pareto frontier. 5. Provide a cost structure which can capture multiple key probability distribution parameters of edge variables. This is in contrast with usual techniques which just capture single parameters like the mean or the variance of distributions. 6. Provide a MIP formulation to a multi-commodity transportation problem with multiple decision variables, stochastic demands and uncertain edge/route capacities. 7. Provide an alternate formulation to the classic binary facility selection problem.

Thesis (Ph. D.)--York University, 2002. Graduate Programme in Physics and Astronomy. / Typescript. Includes bibliographical references (leaves 111-116). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ76023.