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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.
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...
We develop an adaptive spectral element method to price American options, whose solutions contain a moving singularity, automatically and to within prescribed errors. The adaptive algorithm uses an error estimator to determine where...
This dissertation is a study of the Hardy-Lorentz spaces Hp, q for indices in the range 0 < p < 1, 0 < q ≤ ∞. More precisely, for p as indicated, we describe the dual spaces and Banach envelopes of the spaces Hp, q for finite values of q...
Calibration of Multivariate Generalized Hyperbolic Distributions Using the EM Algorithm, with Applications in Risk Management, Portfolio Optimization and Portfolio Credit Risk
The distributions of many financial quantities are well-known to have heavy tails, exhibit skewness, and have other non-Gaussian characteristics. In this dissertation we study an especially promising family: the multivariate generalized...
The objective of this dissertation is to study impulse control problems in situations where the volatility of the underlying process is not constant. First, we explore the case where the dynamics of the underlying process are modified...
It is well-established that distributions of financial returns are heavy-tailed and exhibit skewness and other non-Gaussian characteristics. As time series, return data have volatilities that vary over time and show profound serial...
The main result in this thesis bounds the combinatorial modulus of a ring in a triangulation graph in terms of the modulus of a related ring. The bounds depend only on how the rings are related and not on the rings themselves. This may...
In 1920, Myrberg [23] presented a method for the numerical uniformization of hyperelliptic curves. His ingenious method is based on iterating opening certain slots. He obtains the uniformization as a limit of such a process. Myrberg...
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...
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...
We develop partial differential equation methods with well-posed boundary conditions to price average strike options and swing options in the energy market. We use the energy method to develop boundary conditions that make a two space...
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