Search

Fall 2021

Cao, Han

Risk can be decomposed along two dimensions: risk allocation and risk attribution. On the one hand, the total risk of a company can be allocated to its divisions, using that the company’s profit/loss is the sum of the divisions’ profits/losses. On the other hand, risk is attributed to risk...

Fall 2021

Agrawal, Nishant

In this thesis, we study the product formula for finitely many multiple Itˆo-Wiener integrals of Levy process, option pricing formula where the stock price is modelled by stochastic delay differential equation (SDDE) driven by Levy process and logarithmic Euler-Maruyama scheme for the SDDE. In...

Fall 2021

Xie, Haihan

This thesis proposes a novel Gaussian copula function-on-scalar regression, which is more flexible to characterize the relationship between functional or image response and scalar predictors and is able to relax the linear assumption in traditional function-on-scalar linear regression. Estimation...

Fall 2021

Kosakian, Aslan

Hydrogen fuel cells convert the chemical energy of hydrogen directly into electricity, with the only byproducts being heat and water. The high cost of hydrogen fuel cells due to the expensive platinum catalyst is one of the limiting factors to their global commercialization. Improving fuel-cell...

Fall 2021

Hongxi, Wan

Imposing a constraint on the initial wealth may cause the perfect hedging impossible. In this case, the goal of an investor is to find a strategy that minimize the shortfall under a certain measure, which leads to the concept of partial hedging. In this thesis, the shortfall risk is measured by...

Spring 2021

Wei Tu

Envelopes, introduced by Cook et al. (2007), encompass a class of methods for increasing efficiency in multivariate analyses without altering traditional objectives. Envelopes have been successfully incorporated to a variety of regression models from generalized linear models to quantile...

Fall 2021

Wang, Yibo

A great deal of statistical research has been done in high- and ultrahigh-dimensional settings in recent years. Regularized approaches have been extensively used in dealing with high-dimensional datasets. It is widely acknowledged that robust procedures are important to deal with the influence of...

Fall 2021

Ge, Yan

This thesis consists of the following two parts: In the first part, we investigate the relationship between positive definite functions on the unit sphere and in the Euclidean space with the same dimensions. For the dimension d is odd, a new technique is developed to establish the inheritance of...

Spring 2021

Lu, Ran

Generalizing wavelets by adding desired redundancy and flexibility, framelets (a.k.a. wavelet frames) are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing moments for sparse multi-scale...

Fall 2021

Budinski, Paul Garrett

The majority of known examples of fusion categories come directly from classical structures -- vector spaces, groups, representations, and the like. In recent years the technique of constructing fusion categories as endomorphisms on Cuntz algebras was developed and has already lead to completely...