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Skip to Search Results 7Frei, Christoph (Mathematical and Statistical Sciences)
 7Kong, Linglong (Mathematical and Statistical Sciences)
 7Lewis, Mark (Mathematical and Statistical Sciences)
 6Han, Bin (Mathematical and Statistical Sciences)
 6Hillen, Thomas (Mathematical and Statistical Sciences)
 6Mizera, Ivan (Mathematical and Statistical Sciences)

Fall 2023
As one type of principalagent 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 continuoustime model in...

Fall 2022
Interface problems arise in many applications such as modeling of underground waste disposal, oil reservoirs, composite materials, and many others. The coefficient $a$, the source term $f$, the solution $u$ and the flux $a\nabla u\cdot \vec{n}$ are possibly discontinuous across the interface...

Fall 2022
In this dissertation, various problems related to stochastic (partial) differential equations are investigated. These problems include wellposedness, H\"older continuity of the solution, moments of the solution and their asymptotics. This thesis is divided into three parts. The first part...

Beyond Static Classification: Longterm Fairness for Minority Groups via Performative Prediction and Distributionally Robust Optimization
DownloadFall 2022
In recent years machine learning (ML) models have begun to be deployed at enormous scales, but too often without adequate concern for whether or not an ML model will make fair decisions. Fairness in ML is a burgeoning research area, but work to define formal fairness criteria has some serious...

Fall 2022
Numerous studies have been devoted to the estimation and inference problems for functional linear models (FLM). However, few works focus on model checking problem that ensures the reliability of results. Limited tests in this area do not have tractable null distributions or asymptotic analysis...

Fall 2022
The topological recursion is a construction in algebraic geometry that takes in the data of a socalled spectral curve, $\mathcal{S}=\left(\Sigma,x,y\right)$ where $\Sigma$ is a Riemann surface and $x,y:\Sigma\to\mathbb{C}_\infty$ are meromorphic, and recursively constructs correlators which, in...

Fall 2022
Numerical methods are one of the most important aspects in the computer modelling of physical phenomena governed by differential equations. In order to study these phenomena precisely and in a timely manner, we need to use robust and efficient numerical methods for solving the underlying...

Fall 2022
We consider the category of modules over certain subalgebras of the unrolled restricted quantum group associated to any reductive Lie algebra and show some progress towards the proof of an equivalence of categories of this with the category of local representations of a simple current extension.

Fall 2022
Convolution Neural Networks (CNNs) have rapidly evolved since their neuroscience beginnings. These models efficiently and accurately classify images by optimizing the model’s hidden representations to these images through training. These representa tions have been shown to resemble neural data...

Reflected Backward Stochastic Differential Equations for Informational Systems with Applications
DownloadSpring 2022
The core innovation of this thesis lies in studying reflected backward stochastic differential equations (RBSDE hereafter) for informational systems. An informational system is a system where there is discrepancy in the information received by agents over time. In this thesis, we restrict to the...