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Fall 2014

Tan, Xiaobai

Given an algebraic group G over a field k and a k-algebra R, the role of maximal abelian k-diagonalizable subalgebras (MAD for short) of G(R) is the same as that the split maximal torus play in G(k). Let G be a reductive group such that the derived subgroup is simply connected and let Spec(R) be...

Fall 2013

Ma, Junfeng

This thesis develops three major essays on the topic of horizon-dependence for optimal portfolio. The first essay contributes extensively to the newest concept of forward utilities. In this essay, we describe explicitly three classes of forward utilities--that we call HARA forward utilities--as...

Fall 2010

Zhuang, Xiaosheng

In Chapters 1 and 2, we introduce the definition of interpolating refinable function vectors in dimension one and high dimensions, characterize such interpolating refinable function vectors in terms of their masks, and derive their sum rule structure explicitly. We study biorthogonal refinable...

Fall 2012

Daemi, Maryam

This dissertation first reviews the construction of an optimal design for a straight linear regression model with uncorrelated errors when the experimenter seeks protection against the biases which will accrue if her straight line model is slightly erroneous. The optimal design is derived from...

Spring 2015

Goswami, Souvik

For a smooth projective variety defined over a number field, Beilinson (and independently Bloch) constructed a `height' pairing under very reasonable assumptions and with a number of conjectural properties. A folklore conjecture related to this pairing states that the rational Griffiths...

Fall 2009

Deng, Jian

Computation methods based on the Wiener chaos expansion have been developed to study the behaviors of the aeroelastic system with randomparameters. It is proven that the discrete wavelet transformation is one ofthe most accurate and efficient numerical schemes for this uncertainty...

Spring 2016

Zhang,Zecheng

A cell centered finite difference scheme for 2D parabolic problems on grids with a local refinement is presented. Peaceman and Rachford directional splitting is used in the discretization of time. The scheme is unconditionally stable and proven to be of second order convergence in time. Numerical...

Fall 2009

Li, Hao

Black-Scholes Model is a widely used mathematical model for stock price behaviors, of which the return is assumed to be normally distributed. But this 'normally distributed' assumption is doubted and proved to be not true by realistric data. The main goal of this thesis is to explore...

Spring 2015

Zou, Bin

Motivated by the financial crisis of 2007-2009 and the increasing demand for portfolio and risk management, we study optimal insurance and investment problems with regime switching in this thesis. We incorporate an insurable risk into the classical consumption and investment framework and...

Fall 2013

Yang, Zhuolin

This thesis considers PVol (Percentage of Volume) strategies, which are an often used type of algorithmic trading strategies. In a PVol strategy, the broker aims to bring the order execution speed in line with a percentage of the market volume. This target percentage and the total order size are...