Physical Sciences and Mathematics Commons^™

Applications Of Stochastic Calculus To Finance, Scott Stelljes

UNF Graduate Theses and Dissertations

Stochastic Calculus has been applied to the problem of pricing financial derivatives since 1973 when Black and Scholes published their famous paper "The Pricing of Options and Corporate Liabilities" in the Joumal of Political Economy. The purpose of this thesis is to show the mathematical principles underlying the methods applied to finance and to present a new model of the stock price process.

As part of this paper, we present proofs of Ito's Formula and Girsanov's Theorem which are frequently used in financial applications. We demonstrate the application of these theorems to calculating the fair price of a European call …

Robust I-Sample Analysis Of Means Type Randomization Tests For Variances, Anthony Joseph Bernard

UNF Graduate Theses and Dissertations

The advent of powerful computers has brought about the randomization technique for testing statistical hypotheses. Randomization tests are based on shuffles or rearrangements of the (combined) sample. Putting each of the I samples "in a bowl" forms the combined sample. Drawing samples "from the bowl" forms a shuffle. Shuffles can be made with or without replacement.

In this thesis, analysis of means type randomization tests will be presented to solve the homogeneity of variance problem. An advantage of these tests is that they allow the user to graphically present the results via a decision chart similar to a Shewhart control …

An Efficient Implementation Of The Transportation Problem, Alissa Michele Sustarsic

UNF Graduate Theses and Dissertations

The transportation problem is a special type of linear program in which the objective is to minimize the total cost of shipping a single commodity from a number of sources (m) to a number of destinations or sinks (n).

Because of the special structure of the transportation problem, a special algorithm can be designed to find an optimal solution efficiently. Due to the large amount of information in the problem, judicious storage and management of the data are essential requirements of any viable implementation of the transportation algorithm.

Using sparse matrix techniques to store the solution …

A Bayesian Meta-Analysis Using The Gibbs Sampler, Shannon Marie Fair

UNF Graduate Theses and Dissertations

A meta-analysis is the combination of results from several similar studies, conducted by different scientists, in order to arrive at a single, overall conclusion. Unlike common experimental procedures, the data used in a meta-analysis happen to be the descriptive statistics from the distinct individual studies.

In this thesis, we will consider two regression studies performed by two scientists. These studies have one common dependent variable, Y, and one or more independent common variables, X. A regression of Y on X with other independent variables is carried out on both studies. We will estimate the regression coefficients of X …

A General Theory Of Geodesics With Applications To Hyperbolic Geometry, Deborah F. Logan

UNF Graduate Theses and Dissertations

In this thesis, the geometry of curved surfaces is studied using the methods of differential geometry. The introduction of manifolds assists in the study of classical two-dimensional surfaces. To study the geometry of a surface a metric, or way to measure, is needed. By changing the metric on a surface, a new geometric surface can be obtained. On any surface, curves called geodesics play the role of "straight lines" in Euclidean space. These curves minimize distance locally but not necessarily globally. The curvature of a surface at each point p affects the behavior of geodesics and the construction of geometric …

Monte Carlo Methods For Confidence Bands In Nonlinear Regression, Shantonu Mazumdar

UNF Graduate Theses and Dissertations

Confidence Bands for Nonlinear Regression Functions can be found analytically for a very limited range of functions with a restrictive parameter space. A computer intensive technique, the Monte Carlo Method will be used to develop an algorithm to find confidence bands for any given nonlinear regression functions with a broader parameter space.

The logistic regression function with one independent variable and two parameters will be used to test the validity and efficiency of the algorithm. The confidence bands for this particular function have been solved for analytically by Khorasani and Milliken (1982). Their derivations will be used to test the …

Density Of The Numerators Or Denominators Of A Continued Fraction, Seyed J. Vafabakhsh

UNF Graduate Theses and Dissertations

Let A = {a_n}^∞_{n = 1} be a sequence of positive integers. There are two related sequences P_n and Q_n obtained from A by taking partial convergents out of the number [0; a₁, a₂, ..., a_n, ...], where P_n and Q_n are the numerators and denominators of the finite continued fraction [0; a₁, a₂, ...,a_n].

Let P(n) be the largest positive integer k , such that P_k ≤ n. The sequence Q(n …

A Study Of The Two Major Causes Of Neonatal Deaths: Perinatal Conditions And Congenital Anomalies, Felipe Lorenzo-Luaces

UNF Graduate Theses and Dissertations

Infant mortality is a public health concern in the United states. We concentrate on neonatal mortality for its high accountability of infant mortality. In this paper we study the neonatal mortality of Florida's 1989 live birth cohort.

The data has been analyzed for two major causes of deaths: perinatal conditions and congenital anomalies. We use the KAPLAN-MEIER method to estimate the survival probabilities. For each cause, data were fit to the Weibull models and Extreme Value models to estimate the parameters of the survival curves. The results indicate that primary factors for each cause of neonatal deaths are very low …

Statistical Analysis Of Survival Data, Rexanne Marie Bruno

UNF Graduate Theses and Dissertations

The terminology and ideas involved in the statistical analysis of survival data are explained including the survival function, the probability density function, the hazard function, censored observations, parametric and nonparametric estimations of these functions, the product limit estimation of the survival function, and the proportional hazards estimation of the hazard function with explanatory variables.

In Appendix A these ideas are applied to the actual analysis of the survival data for 54 cervical cancer patients.

A Relationship Between The Fibonacci Sequence And Cantor's Ternary Set, John David Samons

UNF Graduate Theses and Dissertations

The Fibonacci sequence and Cantor's ternary set are two objects of study in mathematics. There is much theory published about these two objects, individually. This paper provides a fascinating relationship between the Fibonacci sequence and Cantor's ternary set. It is a fact that every natural number can be expressed as the sum of distinct Fibonacci numbers. This expression is unique if and only if no two consecutive Fibonacci numbers are used in the expression--this is known as Zekendorf's representation of natural numbers. By Zekendorf's representation, a function F from the natural numbers into [0,0.603] will be defined which has the …

Regression Trees Versus Stepwise Regression, Mary Christine Jacobs

UNF Graduate Theses and Dissertations

Many methods have been developed to determine the "appropriate" subset of independent variables in a multiple variable problem. Some of the methods are application specific while others have a wide range of uses. This study compares two such methods, Regression Trees and Stepwise Regression. A simulation using a known distribution is used for the comparison. In 699 out of 742 cases the Regression Tree method gave better predictors than the Stepwise Regression procedure.

A Study Of The Survival Rate Of The Hepatitis B Virus, James Abraham Houck Iii

UNF Graduate Theses and Dissertations

Hepatitis B virus (HBV) is one of many viruses transmitted through the blood or body fluids. This paper concentrates on a mathematical study of the survival rate of HBV. Using data which includes the survival time for individuals who were diagnosed as being affected by HBV and those who died from HBV, we fit non-linear models to study the survival time for people affected by the virus. Survival probabilities suggest an exponential curve for the survival time. We also consider a pure death process which is a stochastic model for the survival time of the individuals affected. Our results show …

The Linear Least Squares Problem Of Bundle Adjustment, Joseph Walker Woodard

UNF Graduate Theses and Dissertations

A method is described for finding the least squares solution of the overdetermined linear system that arises in the photogrammetric problem of bundle adjustment of aerial photographs. Because of the sparse, blocked structure of the coefficient matrix of the linear system, the proposed method is based on sparse QR factorization using Givens rotations. A reordering of the rows and columns of the matrix greatly reduces the fill-in during the factorization. Rules which predict the fill-in for this ordering are proven based upon the block structure of the matrix. These rules eliminate the need for the usual symbolic factorization in most …

Identifying Outliers In A Random Effects Model For Longitudinal Data, Tamarah Crouse Dishman

UNF Graduate Theses and Dissertations

Identifying non-tracking individuals in a population of longitudinal data has many applications as well as complications. The analysis of longitudinal data is a special study in itself. There are several accepted methods, of those we chose a two-stage random effects model coupled with the Estimation Maximization Algorithm (E-M Algorithm) . Our project consisted of first estimating population parameters using the previously mentioned methods. The Mahalanobis distance was then used to sequentially identify and eliminate non-trackers from the population. Computer simulations were run in order to measure the algorithm's effectiveness.

Our results show that the average specificity for the repetitions for …