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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)
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Spring 2023
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...
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Spring 2023
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...
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A General Framework of Optimal Stochastic Optimization with Dependent Data: Multiple Optimality Guarantee, Sample Complexity, and Tractability
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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...
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Spring 2023
Since the COVID-19 outbreak in Wuhan City in December 2019, numerous model predictions on the COVID-19 epidemics in Wuhan have been reported. These model predictions have shown a wide range of variations. In our first study, we demonstrate that nonidentifiability in model calibrations using the...
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Fall 2023
Distributions of sequences modulo one (mod 1) have been studied over the past century with applications in algebra, number theory, statistics, and computer science. For a given sequence, the weak convergence of the associated empirical distributions has been the usual approach to these studies....
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Nonlinear Evolution of Localized Internal Gravity Wave Packets: Theory and Simulations with Rotation, Background Flow, and Anelastic Effects
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A series of three studies investigates theoretically and numerically the evolution, stability, and pseudomomentum transport of fully localized three-dimensional internal gravity wave packets, as they self-interact nonlinearly with their induced mean flow. The first study considers a rotating,...
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Global dynamics of diffusive animal movement models under habitat degradation, destruction, and fragmentation: eigenvalue problems and geometry at the landscape scale
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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...
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Spring 2023
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...
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Spring 2023
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...