Physical Sciences and Mathematics Commons^™

Studies Of Contingent Capital Bonds, Jingya Li

Electronic Thesis and Dissertation Repository

A contingent capital bond (CCB) is a subordinated security that converts to common shares when a predetermined trigger is breached. The 2008 financial crisis and the Basel III motivate the issuance of CCBs, aiming to mitigate the too-big-to-fail problem in financial distress and to resolve financial institutions by bailing in with the firm’s own capital rather than a bailing out using the taxpayers’ money.

Within the structural modelling framework, we consider the pricing of CCBs with an affine geometric Brownian motion by assuming that coupon payments have impact on the asset value dynamics. We extend the capital structure into four …

Evolution Of Mobile Promoters In Prokaryotic Genomes., Mahnaz Rabbani

Electronic Thesis and Dissertation Repository

Mobile genetic elements are important factors in evolution, and greatly influence the structure of genomes, facilitating the development of new adaptive characteristics. The dynamics of these mobile elements can be described using various mathematical and statistical models. In this thesis, we focus on a specific category of mobile genetic elements, i.e. mobile promoters, which are mobile regions of DNA that initiate the transcription of genes. We present a class of mathematical models for the evolution of mobile promoters in prokaryotic genomes, based on data obtained from available sequenced genomes. Our novel location-based model incorporates two biologically meaningful regions of the …

Secondary Electrohydrodynamic Flow Generated By Corona And Dielectric Barrier Discharges, Mohammadreza Ghazanchaei

Electronic Thesis and Dissertation Repository

One of the main goals of applied electrostatics engineering is to discover new perspectives in a wide range of research areas. Controlling the fluid media through electrostatic forces has brought new important scientific and industrial applications. Electric field induced flows, or electrohydrodynamics (EHD), have shown promise in the field of fluid dynamics. Although numerous EHD applications have been explored and extensively studied so far, most of the works are either experimental studies, which are not capable to explain the in depth physics of the phenomena, or detailed analytical studies, which are not time effective. The focus of this study is …

Tropical Cyclone Wind Hazard Assessment For Southeast Part Of Coastal Region Of China, Sihan Li

Electronic Thesis and Dissertation Repository

Tropical cyclone (TC) or typhoon wind hazard and risk are significant for China. The return period value of the maximum typhoon wind speed is used to characterize the typhoon wind hazard and assign wind load in building design code. Since the historical surface observations of typhoon wind speed are often scarce and of short period, the typhoon wind hazard assessment is often carried out using the wind field model and TC track model. For a few major cities in the coastal region of mainland China, simple or approximated wind field models and a circular subregion method (CSM) have been used …

The Effect Of Diversification On The Dynamics Of Mobile Genetic Elements In Prokaryotes: The Birth-Death-Diversification Model, Nicole E. Drakos

Electronic Thesis and Dissertation Repository

Mobile genetic elements (MGEs) are ubiquitous among prokaryotes, and have important implications to many areas, such as the evolution of certain genes, bioengineering and the spread of antibiotic resistance. In order to understand the complex dynamics of MGEs, mathematical models are often used. One model that has been used to describe the dynamics of mobile promoters (a class of MGEs) is the birth-death-diversification model. This model is unique in that it allows MGEs to diversify to create new families. In this thesis, I analyze the dynamics of this model; in particular, I examine equilibrium distributions, extinction probabilities and mean time …

Algorithms To Compute Characteristic Classes, Martin Helmer

Electronic Thesis and Dissertation Repository

In this thesis we develop several new algorithms to compute characteristics classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (CSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).

We begin with subschemes of a projective space over an algebraically closed field of characteristic zero. In this setting we give effective algorithms to compute the CSM class, Segre class and …

Extensions Of The Cross-Entropy Method With Applications To Diffusion Processes And Portfolio Losses, Alexandre Scott

Electronic Thesis and Dissertation Repository

Rare event simulation is a crucial part of simulations. In financial mathematics, the study of rare events appear naturally when we consider risk measures such as the conditional value at risk. This thesis is composed of three related papers treating the rare event simulations subject: the first paper addresses rare event simulations using for diffusion processes, the second paper addresses rare event simulations for the normal and the Student t-copula model while the last paper addresses rare event simulations for a portfolio model where there is a correlation structure between the loss-given-default and the probability of default.

Determination Of Lie Superalgebras Of Supersymmetries Of Super Differential Equations, Xuan Liu

Electronic Thesis and Dissertation Repository

Superspaces are an extension of classical spaces that include certain (non-commutative) supervariables. Super differential equations are differential equations defined on superspaces, which arise in certain popular mathematical physics models. Supersymmetries of such models are superspace transformations which leave their sets of solutions invariant. They are important generalization of classical Lie symmetry groups of differential equations.

In this thesis, we consider finite-dimensional Lie supersymmetry groups of super differential equations. Such supergroups are locally uniquely determined by their associated Lie superalgebras, and in particular by the structure constants of those algebras. The main work of this thesis is providing an algorithmic method …