Physical Sciences and Mathematics Commons^™

First-Passage Time Models With A Stochastic Time Change In Credit Risk, Hui Li

Theses and Dissertations (Comprehensive)

Many authors have used a time-changed Brownian motion as a model of log-stock returns. Using a Levy process as a stochastic time change, one obtains well known asset price models such as the variance gamma (VG) and normal inverse Gaussian (NIG) models. Following on the heels of these asset price models, it is natural to extend structural credit models by using a time-changed geometric Brownian motion and other jump-diffusion processes to model the value of a firm. To avoid the difficulties that arise in computing the associated first passage time distribution and in analogy to the time-changed Markov chain models, …

Mathematical Modeling Of Quantum Dots With Generalized Envelope Functions Approximations And Coupled Partial Differential Equations, Dmytro Sytnyk

Theses and Dissertations (Comprehensive)

No abstract provided.

Simulation Studies On Estimation Of Variance Components For Multilevel Models, Sara Vakilian

Theses and Dissertations (Comprehensive)

With the presence of unequal sampling in a multilevel model, the weight inflated estimators for variance components can be biased even though the use of survey weights results in design consistent estimators of the parameters. In this thesis I will carry out a simulation study to examine the performance of current existing methods and I will examine the resampling method for correcting bias of estimators of variance components of a multilevel model with covariates. This study will be based on these three papers: “Weighting for Unequal Selection Probabilities in Multilevel Models” by D. Pfeffermann , C. J. Skinner, D.J. Holmes, …

Applications Of New Diffusion Models To Barrier Option Pricing And First Hitting Time In Finance, Keang Ly

Theses and Dissertations (Comprehensive)

The main focus of this thesis is in the application of a new family of analytical solvable diffusion models to arbitrage-free pricing exotic financial derivatives, such as barrier options. The family of diffusions is the so-called “Drifted Bessel family” having nonlinear (smile-like) local volatility with multiple adjustable parameters. In particular, the drifted Bessel-K diffusion is used to model asset (stock) price processes under a risk-neutral measure whereby discounted asset price are martingales.

Closed-form spectral expansions for barrier option values are derived within the Bessel-K family of models. This follow from the closed-form spectral expansions for the transition probability …

Strict-Dominance Solvability Of Games On Continuous Strategy Spaces, Andrew Campbell Elkington

Theses and Dissertations (Comprehensive)

The concept of strict dominance provides a technique that can be used normatively to predict the play of games based only on the assumption of individual rationality. Such predictions, unlike those based on Nash equilibria, do not depend on players’ beliefs about the behaviour of others. One strategy strictly dominates another if and only if the payoff from the first strategy is strictly greater than the payoff from the second, no matter how the opponent(s) plays. It is possible for iterated elimination of strictly dominated strategies to remove all but a single choice for each player, in which case we …

Models For On-Line Social Networks, Noor Hadi

Theses and Dissertations (Comprehensive)

On-line social networks such as Facebook or Myspace are of increasing interest to computer scientists, mathematicians, and social scientists alike. In such real-world networks, nodes represent people and edges represent friendships between them. Mathematical models have been proposed for a variety of complex real-world networks such as the web graph, but relatively few models exist for on-line social networks.

We present two new models for on-line social networks: a deterministic model we call Iterated Local Transitivity (ILT), and a random ILT model. We study various properties in the deterministic ILT model such as average degree, average distance, and diameter. We …