Search

Spring 2023

Vasilev, Ilia

In present thesis I focus on development of method of market completions and its applications to various problems in pricing and hedging of contingent claims. Since theory of mathematical finance is well developed on complete markets, and corresponding solutions are well understood, method of...

Spring 2023

Xie, Zhangqian

Credit risk management, which deals with mitigating losses from lending activities, is crucial for financial institutions. Hence, credit risk modelling can be employed to reduce potential losses and avoid financial crises. There are sometimes monotonic relationships in credit risk models, which...

Fall 2023

Kettle, Bryan W

This dissertation establishes various structural and representation theoretic results in super Yangian theory. In its first part, this dissertation details the algebraic structure and representation theory for the Yangians of orthosymplectic Lie superalgebras. Addressing these Yangians via the...

Fall 2023

Riesen, Andrew

$G$-structures on fusion categories have been shown to be an important tool to understand orbifolds of vertex operator algebras \cite{Kirillov}\cite{Gcrossedmuger}\cite{Orbifold_Paper}. We continue to develop this idea by generalizing Eilenberg-Maclane's notion of an Abelian $3$-cocycle to...

Fall 2023

Liu, Wenyue

As one type of principal-agent problem, the insurance contract models are closely related to the extent of information disclosure. We construct two new insurance contract models with full information and adverse selection respectively. The full information model is a continuous-time model in...

Fall 2023

Salmaniw, Yurij

Habitat loss is a significant problem and the leading cause of species extinctions and decreases in biodiversity worldwide. This issue is primarily driven by human activities, making it crucial to understand the consequences of our actions as a global community. The empirical study of habitat...

Spring 2023

Pan, Bo

We consider stochastic optimization in settings where the distribution of unknown parameters is observable only through finitely dependent training samples. Using the Sample Averaging Approximation ({SAA}), we specifically study the data-driven procedure in which, instead of receiving samples...

Spring 2023

Wang, Siting

Generative Adversarial Networks (GAN) are a field of popular generating models, and there are many variants these years. Lim and Ye 2017 proposed the Geometric GAN to connect the network with the geometric interpretation. They update the discriminator based on the algorithm of Support Vector...

Spring 2023

Hua, Xiaotian

Coral reefs are essential to the marine ecosystem, and provide some of the most diverse habitats in the world. Coral reef fisheries contribute 6.8 billion to the economy a year globally. However, coral reefs are under significant threat because of human activities such as overfishing, ocean...

Fall 2023

Burak, Katherine

Many standard approaches for conducting statistical inference on regression parameters rely heavily on parametric assumptions and asymptotic results. The wild bootstrap (Mammen, 1993) was developed as a nonparametric means to estimate a sampling distribution and is particularly useful when...