Now showing items 1-8 of 8
ASYMPTOTIC ANALYSIS AND BOUNDS OF MULTIVARIATE COHERENT RISK
A central topic in modern financial and insurance mathematics is the search for new methods to estimate extreme risk (or tail risk) for multivariate financial assets. This research targets this fundamental question about ...
A Nonlinear Stability Analysis of Vegetative Turing Pattern Formation for an Interaction-Diffusion Plant-Surface Water Model System in an Arid Flat Environment
The development of spontaneous stationary vegetative patterns in an arid flat environment is investigated by means of a weakly nonlinear diffusive instability analysis applied to the appropriate model system for this ...
Simplicial Complexes and the Optimal Homologous Chain Problem
This dissertation examines topological properties of a finite simplicial complex
Mathematical models of species' responses to habitat destruction
Anthropogenic habitat destruction is the leading cause of the high rate of extinctions of species observed around the world today. With a growing human population, it is vitally important for conservationists to understand ...
TAIL MUTUAL INFORMATION OF VINE COPULAS
Multivariate mutual information describes the amount of uncertainty among several random variables, whose scale-invariant dependence is captured by the copula of the joint distribution. In this dissertation, we first show ...
Portfolio Optimization on Jump Diffusion
Portfolio optimization problem is an important research topic in financial applications. In this research, we focus on a consumption process and a terminal wealth problem. A portfolio including a riskless asset, a zero ...
CONTRIBUTIONS TO THE THEORY OF SEMIDEFINITE PROGRAMMING UNDER UNCERTAINTY
Stochastic semidefinite programs (SSDPs) were introduced recently as a natural extension of two-stage stochastic linear programs and of semidefinite programs. Theoretical results for stochastic linear programs (SLPs) and ...
EXPERIMENTS IN MEDICAL IMAGE SEGMENTATIONS
Non-invasive Radiology Imaging (e.g. CT, MRI, and PET) have been utilized tremendously in medical study for disease diagnosis, prognostication, and monitoring therapeutic response. And segmenting medical image for regions ...