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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.
This dissertation consists of two parts. In the first part we present a quasi-Monte Carlo implementation of the de-biased Monte Carlo estimator in the context of stochastic differential equations. We combine the quasi-Monte Carlo...
In financial markets under uncertainty, the classical Black-Scholes model cannot explain the empirical facts such as fat tails observed in the probability density. To overcome this drawback, during the last decade, Lévy process and...
This work develops both the theoretical foundation and the practical application of random Sobol' analysis with two goals. The first is to provide a more general and accommodating approach to global sensitivity analysis, in which the...
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...
According to rapid development in information technology, limit order books(LOB) mechanism has emerged to prevail in today's nancial market. In this paper, we propose ensemble machine learning architectures for capturing the dynamics of...
In this dissertation, methods of estimating the sensitivity of complex exotic options, including options written on multiple assets, and have discontinuous payoffs, are investigated. The calculation of the sensitivities (Greeks) is based...
GPU computing has become popular in computational finance and many financial institutions are moving their CPU based applications to the GPU platform. We explore efficient implementations for two main financial problems on GPU: pricing, ...
The financial market is modelled as a complex self-organizing system. Three economic agents interact in a simplified economy and seek the maximization of their wealth. Replicator dynamics are used as a myopic behavioral rule to describe...
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...
Randomized quasi-Monte Carlo (RQMC) methods were first developed in mid 1990’s as a hybrid of Monte Carlo and quasi-Monte Carlo (QMC) methods. They were designed to have the superior error reduction properties of low-discrepancy...
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...
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...
In this dissertation, we create three theoretical models to answer questions raised by recent experiments that lie beyond the scope of current theory. In the landmark-effect model, we determine size, shape and location for a territory...
The problem of optimal portfolio execution has become one of the most important problems in the area of financial mathematics. Over the past two decades, numerous researchers have developed a variety of different models to address this...
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...
In this dissertation, we present several applications of polynomial chaos in Monte Carlo simulation.First, we investigate the use of polynomial chaos as a control variate method for Monte Carlo simulation. Specically, we analyze the mean...
Option pricing by the Fourier method has been popular for the past decade, many of its applications to Lévy processes has been applied especially for European options. This thesis focuses on exponential convergence Fourier method and its...
Iterative methods are widely used to solve algebraic equations and matrix equations. In fact, they can also be used to solve differential equations. Unlike discretization methods which generate point solutions, iterative methods generate...
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