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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
In this dissertation, we evaluate existing Monte Carlo estimators and develop new Monte Carlo estimators for pricing financial options with the goal of improving precision. In Chapter 2, we discuss the conditional expectation Monte Carlo...
The objective of this dissertation is to study the queuing and point process models that try to capture as many features as possible of the high-frequency data of a limit order book. First, we use a generalized birth-death stochastic...
This dissertation investigates asymptotic behaviour of convection in a fluid saturated porous medium. We analyse the Darcy-Boussinesq system under perturbation of the Darcy-Prandtl number parameter. In very tightly packed media this...
Two numerical methods are developed and analyzed for studying two-phase jet flows. The first numerical method solves the eigenvalue problem for the matrix system that is constructed from the pseudo-spectral discretization of the 3D...
In this dissertation, we build a compartment model to investigate the dynamics of spread of dengue fever in both human and mosquito populations. We study the demographic factors that influence equilibrium prevalence, and perform a...
A lot of attention has been paid to the stochastic volatility model where the volatility is randomly fluctuating driven by an additional Brownian motion. In our work, we change the mean level in the mean-reverting process from a constant...
This dissertation develops and evaluates a high order method to compute wave scattering from moving boundaries. Specifically, we derive and evaluate a Discontinuous Galerkin Spectral elements method (DGSEM) with Arbitrary Lagrangian-...
In this dissertation, we discuss the generation of low discrepancy sequences, randomization of these sequences, and the transformation methods to generate normally distributed random variables. Two well known methods for generating...
The work in this thesis is motivated by the application of spray combustion. If one develops algorithms to simulate spray generation, for example the primary break-up of a liquid jet in a gas cross-flow, then a body-fitted or Lagrangian...
This dissertation explores wildfire dynamics. Chapters 2 and 3 are peer reviewed journal articles that present an understanding of three-dimensionality in grass fires and how it affects forward rate of spread (ROS) of the fire. In...
In this dissertation, the coupling phenomenon of porous media flow and free flow is extensively studied, with an application to studying the solute transport in the groundwater system of karst aquifers. This dissertation consists of...
The brain is one of nature's greatest mysteries. The mechanism by which the folds of the brain's cerebral cortex, called gyri (hills) and sulci (valleys), are formed remains unknown. Existing biological hypotheses that attempt to explain...
There are two themes in this thesis: local volatility models and their calibration, and Proper Orthogonal Decomposition (POD) reduced order modeling with application in stochastic volatility models, which has a potential in the...
In this work we quantify the effect of uncertainty in volatility in the prices and Deltas of an American and European put using probabilistic uncertainty analysis. We review the current methods of uncertainty analysis including worst...
This dissertation develops a nonstandard approach to probability, stochastic calculus and financial modeling, within the framework of the Radically Elementary Probability Theory of Edward Nelson. The fundamental objects of investigation...
We price and hedge different financial derivatives with sharp profiles by solving the corresponding advection-diffusion-reaction partial differential equation using new high resolution finite difference schemes, which show superior...
Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.