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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...
Since the scientific study of birdsong began in the late 1950s, songbirds have emerged as impressive neurobiological models for aspects of human verbal communication because they learn to sequence their song elements, analogous, in many...
This paper presents an analysis of the capital needs, needed return on capital, and optimum reinsurance retention for insurance companies, all in the context where claims are either paid out or known with certainty within or soon after...
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...
This thesis presents a new structural framework for multidimensional default risk. The time of default is the first jump of the log-returns of the stock price of a firm below a stochastic default level. When the stock price is an...
This dissertation considers the generalization of two well-known unconstrained optimization algorithms for Rn to solve optimization problems whose constraints can be characterized as a Riemannian manifold. Efficiency and effectiveness...
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...
This dissertation generalizes three well-known unconstrained optimization approaches for Rn to solve optimization problems with constraints that can be viewed as a d-dimensional Riemannian manifold to obtain the Riemannian Broyden family...
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...
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...
The sensitivity analysis of options is as important as pricing in option theory since it is used for hedging strategies, hence for risk management purposes. This dissertation presents new sensitivities for options when the underlying...
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 develop a spectral element method to price European options under the Black-Scholes model, Merton's jump diffusion model, and Heston's stochastic volatility model with one or two assets. The method uses piecewise high order Legendre...
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