Numerical Analysis and Computation Commons^™

Estimation Of Multivariate Asset Models With Jumps, Angela Loregian, Laura Ballotta, Gianluca Gianluca Fusai, Marcos Fabricio Perez

Business Faculty Publications

We propose a consistent and computationally efficient two-step methodology for the estimation of multidimensional non-Gaussian asset models built using Levy processes. The proposed framework allows for dependence between assets and different tail behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets as it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail …

Stair Climbing Hand Truck, James Mcpherson

All Undergraduate Projects

Abstract

Getting a heavy object up a flight of stairs usually requires a team of two or more people. Even with a team of people, the task is often still difficult, dangerous, and possibly insurmountable by one person. This problem is especially prevalent in for those who are moving into apartment complexes. Most apartment complexes have many buildings with two or more floors of living quarters, and elevators are often missing. This project sought to offer a solution to this problem. The solution in question; a motorized hand-truck with 2, trigonal planar pinwheels in place of the stock wheels. The …

Numerical Simulations For Optimal Control Of A Cancer Cell Model With Delay, Jessica S. Lugo

Murray State Theses and Dissertations

Mathematical models are often created to analyze the complicated behavior of many physical systems. One such system is that of the interaction between cancer cells, the immune system, and various treatments such as chemotherapy, radiation, and immunotherapy. Using models that depict these relationships gives researchers insight on the dynamics of this complicated system and possibly ideas for improved treatment schedules.

The model presented here gives the relationship of cancer cells in development phases with immune cells and cycle-specific chemotherapy treatment. This model includes a constant delay term in the mitotic phase. Optimal control theory is used to minimize the cost …

Pawnee Dam Inflow Design Flood (Idf) Update And Stage-Frequency Curve Development Using Rmcrfa, Jennifer P. Christensen, Joshua J. Melliger

United States Geological Survey: Water Reports and Publications

Pawnee Dam is one of the ten Salt Creek Dams designed and built in the 1960s to mitigate flooding in Lincoln, Nebraska. This short paper illustrates the update of the Pawnee Dam inflow design flood (IDF) through calibration to recent high flow events and the development of its stage-frequency or hydrologic loading curve with the U.S. Army Corps of Engineers’ Risk Management Center Reservoir Frequency Analysis (RMC-RFA) model. The IDF update follows Engineering Regulation 1110-8-2, Inflow Design Flood for Dams and Reservoirs, including unit hydrograph peaking and two antecedent pool elevations. Background information on the original design of the dam …

Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …

A Statistical Investigation Of Stock Market Activity And Instances Of Financial Crime, Elizabeth G. Biggs

Theses and Dissertations

This project aims to identify a possible statistical relationship between the stock market and incidences of financial crime in Illinois, Texas, and Utah through big data analysis techniques using data from the FBI’s Federal Bureau of Investigation’s National Incident-Based Reporting System (NIBRS) database. By analyzing the occurrences of financial crime by location, year, and type in relation to the S&P 500’s percent change in close price on the first day of the calendar year, it will be possible to determine if a statistical relationship exists between the two. In addition, regression analysis was performed in order to predict financial crime …

On The Role Of Ill-Conditioning: Biharmonic Eigenvalue Problem And Multigrid Algorithms, Kasey Bray

Theses and Dissertations--Mathematics

Very fine discretizations of differential operators often lead to large, sparse matrices A, where the condition number of A is large. Such ill-conditioning has well known effects on both solving linear systems and eigenvalue computations, and, in general, computing solutions with relative accuracy independent of the condition number is highly desirable. This dissertation is divided into two parts.

In the first part, we discuss a method of preconditioning, developed by Ye, which allows solutions of Ax=b to be computed accurately. This, in turn, allows for accurate eigenvalue computations. We then use this method to develop discretizations that yield accurate computations …

Randomized Algorithms For Preconditioner Selection With Applications To Kernel Regression, Conner Dipaolo

HMC Senior Theses

The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M^-1A ||_F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which …

Rule Extraction And Insertion To Improve The Performance Of A Dynamic Cell Structure Neural Network, Osama Amhamed Elsarrar

Graduate Theses, Dissertations, and Problem Reports (ETD)

Artificial Neural Networks are extremely useful machine learning tools. They are used for many purposes, such as prediction, classification, pattern recognition, etc. Although neural networks have been used for decades, they are still often not completely understood or trusted, especially in safety and mission critical situations. Typically, neural networks are trained on data sets that are representative of what needs to be learned. Sometimes training sets are constructed in order to train the neural network in a certain way, in order to embed appropriate knowledge. The purpose of this research is to determine if there is another method that can …

Defining Historical Earthquake Rupture Parameters And Proposed Slip Distributions Through Tsunami Modeling In South-Central Chile, Alexander Dolcimascolo

All Master's Theses

Reliable tsunami early warning forecasts rely on accurate initial modeling conditions and interpretations of subduction zone behavior in a multi-century perspective. GPS and seismologic data were introduced this past century to study rupture dynamics in detail, however limited information is known about ruptures that pre-date the 20^th century. I propose a methodology that uses statistics to better understand these pre-20^th century ruptures. This methodology applies the historical and geologic tsunami record as a means to select a suite of tsunami simulations from earthquake source solutions. I chose south-central Chile (46°S to 30°S) to test this new methodology; it …

Approximation Of The Generalized Singular Value Expansion, Matthew Jacob Roberts

Dissertations, Master's Theses and Master's Reports

Let $X$, $Y$, and $Z$ be real separable Hilbert spaces, let $T:X \to Y$ be a compact operator, and let $L:D(L) \to Z$ be a closed and densely defined linear operator. Then the generalized singular value expansion (GSVE) is an expansion that expresses $T$ and $L$ in terms of a common orthonormal basis. Under certain hypotheses on discretization, the GSVE of an approximate operator pair $(T_j,L_j)$, where $T_j:X_j \to Y_j$ and $L_j:X_j \to Z_j$, converges to the GSVE of $(T,L)$. Error estimates establish a rate of convergence that is consistent with numerical experiments in the case of discretization using piecewise …

High Order Bound-Preserving Discontinuous Galerkin Methods And Their Applications In Petroleum Engineering, Ziyao Xu

Dissertations, Master's Theses and Master's Reports

This report contains researches in the theory of high-order bound-preserving (BP) discontinuous Galerkin (DG) method and their applications in petroleum engineering. It contains both theoretical analysis and numerical experiments. The compressible miscible displacements and wormhole propagation problem, arising in petroleum engineering, is used to describe the evolution of the pressure and concentrations of different components of fluid in porous media. The important physical features of concentration and porosity include their boundedness between 0 and 1, as well as the monotone increasing for porosity in wormhole propagation model. How to keep these properties in the simulation is crucial to the robustness …

Discontinuous Galerkin Methods For Convection-Diffusion Equations And Applications In Petroleum Engineering, Nattaporn Chuenjarern

Dissertations, Master's Theses and Master's Reports

This dissertation contains research in discontinuous Galerkin (DG) methods applying to convection-diffusion equations. It contains both theoretical analysis and applications. Initially, we develop a conservative local discontinuous Galerkin (LDG) method for the coupled system of compressible miscible displacement problem in two space dimensions. The main difficulty is how to deal with the discontinuity of approximations of velocity, u, in the convection term across the cell interfaces. To overcome the problems, we apply the idea of LDG with IMEX time marching using the diffusion term to control the convection term. Optimal error estimates in L^infinity(0, T; L^{2 …}

Complex Varieties As Minima, Richard Koss

Masters Theses

We will explore various numeric methods of finding roots of an analytic function over some open set of the complex plane. We will discuss a method of visually observing the roots, a gradient descent method for finding the roots of an analytic function, a gradient descent method for solving systems of analytic functions, and finally a method of descent that uses osculating circles to find roots of an analytic function. Of particular interest to this thesis are roots of complex polynomials. There will be examples, code snippets, and outputs of programs to illustrate all of these methods.

Analysis Of Clmr Trees For European And Asian Option Pricing Under Regime-Switching Jump-Diffusion Models, Yaode Sui

Theses and Dissertations (Comprehensive)

In this paper, we study the convergence rates of the multinomial trees constructed by [Costabile, Leccadito, Massabo and Russo, Journal of Computational and Applied Mathematics, 256 (2014), 152 - 167] for European option pricing under the regime-switching jump-diffusion model, which is named as CLMR tree. We also extend the CLMR tree to the pricing of Asian options under the models. Numerical examples are carried out to confirm the theoretical results and the accuracy of computation.

A Detection And Data Acquisition System For Precision Beta Decay Spectroscopy, Aaron P. Jezghani

Theses and Dissertations--Physics and Astronomy

Free neutron and nuclear beta decay spectroscopy serves as a robust laboratory for investigations of the Standard Model of Particle Physics. Observables such as decay product angular correlations and energy spectra overconstrain the Standard Model and serve as a sensitive probe for Beyond the Standard Model physics. Improved measurement of these quantities is necessary to complement the TeV scale physics being conducted at the Large Hadron Collider. The UCNB, ⁴⁵Ca, and Nab experiments aim to improve upon existing measurements of free neutron decay angular correlations and set new limits in the search for exotic couplings in beta decay. To …

An M^X/G(A,B)/1 Queue With Breakdown And Delay Time To Two Phase Repair Under Multiple Vacation, G. Ayyappan, M. Nirmala

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider an M^x /G(a,b)/1 queue with active breakdown and delay time to two phase repair under multiple vacation policy. A batch of customers arrive according to a compound Poisson process. The server serves the customers according to the “General Bulk Service Rule” (GBSR) and the service time follows a general (arbitrary) distribution. The server is unreliable and it may breakdown at any instance. As the result of breakdown, the service is suspended, the server waits for the repair to start and this waiting time is called as „delay time‟ and is assumed to follow general …

Quasi-Linearization Method With Rational Legendre Collocation Method For Solving Mhd Flow Over A Stretching Sheet With Variable Thickness And Slip Velocity Which Embedded In A Porous Medium, M. M. Khader

Applications and Applied Mathematics: An International Journal (AAM)

The quasi-linearization method (QLM) and the rational Legendre functions are introduced here to present the numerical solution for the Newtonian fluid flow past an impermeable stretching sheet which embedded in a porous medium with a power-law surface velocity, variable thickness and slip velocity. Firstly, due to the high nonlinearity which yielded from the ordinary differential equation which describes the proposed physical problem, we construct a sequence of linear ODEs by using the QLM, hence the resulted equations become a system of linear algebraic equations. The comparison with the available results in the literature review proves that the obtained results via …

Global Range Restricted Gmres For Linear Systems With Multiple Right Hand Sides, Mostafa Eslami

Applications and Applied Mathematics: An International Journal (AAM)

This work concerns the solution of non-symmetric, sparse linear systems with multiple right hand sides by iterative methods. Herein a global version of the range restricted generalized minimal residual method (RRGMRES) is proposed for solving this sort of problems. Numerical results confirm that this new algorithm is applicable.

Analysis Of Batch Arrival Bulk Service Queue With Multiple Vacation Closedown Essential And Optional Repair, G. Ayyappan, T. Deepa

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to analyze an queueing model with multiple vacation, closedown, essential and optional repair. Whenever the queue size is less than , the server starts closedown and then goes to multiple vacation. This process continues until at least customer is waiting in the queue. Breakdown may occur with probability when the server is busy. After finishing a batch of service, if the server gets breakdown with a probability , the server will be sent for repair. After the completion of the first essential repair, the server is sent to the second optional repair with probability …