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Skip to Search Results- 7Frei, Christoph (Mathematical and Statistical Sciences)
- 7Kong, Linglong (Mathematical and Statistical Sciences)
- 7Lewis, Mark (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Hillen, Thomas (Mathematical and Statistical Sciences)
- 6Mizera, Ivan (Mathematical and Statistical Sciences)
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Fall 2016
The aim of my thesis consists of characterizing explicitly the optimal consumption and investment strategy for an investor, when her habit level process is incorporated in the utility formulation. For a continuous-time market model, I maximize the expected utility from terminal wealth and/or...
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Fall 2014
Financial systemic crisis could be broadly understood as the deterioration of the banking sector which results in damage to the real economy. From elementary accounting, a firm's financial position can be characterized by the value of its asset holdings versus the amount it borrow from others. If...
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Option Pricing and Logarithmic Euler-Maruyama Convergence of Stochastic Delay Equations driven by Levy process
DownloadFall 2021
In this thesis, we study the product formula for finitely many multiple Itˆo-Wiener integrals of Levy process, option pricing formula where the stock price is modelled by stochastic delay differential equation (SDDE) driven by Levy process and logarithmic Euler-Maruyama scheme for the SDDE. In...
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Optional Processes and their Applications in Mathematical Finance, Risk Theory and Statistics
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This thesis is dedicated to the study of the general class of random processes, called optional processes, and their various applications in Mathematical Finance, Risk Theory, and Statistics. First, different versions of a comparison theorem and a uniqueness theorem for a general class of...
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Spring 2014
It is well known that the normal return estimation for financial asset prices is defective. In order to find better models to estimate the prices behavior of financial assets, people need probabilistic distribution that can capture fat-tails, non-constant moments, etc. This thesis find some...
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Fall 2023
This dissertation establishes various structural and representation theoretic results in super Yangian theory. In its first part, this dissertation details the algebraic structure and representation theory for the Yangians of orthosymplectic Lie superalgebras. Addressing these Yangians via the...
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Outer Products and Stochastic Approximation Algorithms in a Heavy-tailed and Long-range Dependent Setting
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Classical time-series theories are mainly concerned with the statistical analysis of light-tailed and short-range dependent stationary linear processes. Applications in network theory and financial mathematics lead us to consider time series models with heavy tails and long memory. Heavy-tailed...
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Parameter Estimation of Mathematical Models: Estimation of the Burden of HIV Epidemics as a Case Study
DownloadFall 2016
Mathematical models are widely used to describe dynamics in various fields. In practice, it is necessary and important to determine model parameters based on existing data. A major challenge for parameter estimation under modeling framework lies in non-identifiability issue: parameter values on a...
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Parsimonious Contaminated Shifted Asymmetric Laplace Mixtures: Unsupervised Learning with Outlier Identification for Asymmetric Clusters in High Dimensions
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A family of parsimonious contaminated shifted asymmetric Laplace mixtures is developed for asymmetric clusters in the presence of outliers and noise (referred to as bad points herein). A series of constraints are applied to a modified factor analyzer structure of the scale matrix parameters,...