Mathematical Sciences 2008 Completed MQPs
Qualitative Behavior of Solutions For Shallow Water Wave
Student:
Abebe, Eyuel D.
Advisor:
LUO, T (MA)
This MQP report concerns the finding of the convergence rates to the equilibrium constant states of shallow water wave equations with relaxation as time goes to infinity and establishing the existence of global in time solutions. We study the initial value problem, under a certain set of initial conditions, by considering the system in Lagrangian coordinates using different transformations. We develop two essential lemmas that we employ to prove the global in time existence of solutions and show, moreover, how these lemmas yield the convergence rates, given the initial conditions. We also look at the general case by strengthening the initial conditions and arrive at another system of equations that is similar to the previous one, the analysis of which follows naturally.
Discussions of No Arbitrage in Financial Markets
Students:
Chase, Tyler A.
Tiu, Michael Anonuevo
Advisor:
SAYIT, H. (MA)
We consider a financial market with one continuous time risky price process and one continuous time risk-free price process. We assume all the trading takes place at finitely many time points in this market. We provide necessary and sufficient conditions on the discounted price process so that the market does not admit arbitrage possibilities.
Portfolio Risk Minimization Using Historical Data
Student:
Duncan, Brian K.
Advisor:
BLAIS, M. (MA)
Data from 1999 was gathered for 90 stocks in the S&P 500. The first 6 months of data was used to create a portfolio with the minimum risk while given an expected rate of return. Constraints were then added to limit short selling and limit the number of shares of certain stocks. The resulting portfolios were then tested to see if their future performance for the next 6 months would have produced a profit.
Multiple Target Tracking
Students:
Connor, Matthew J.
Haas, Kathleen
Volfson, Alexander
Advisor:
ABRAHAM, J.P. (MA)
CLANCY, E.A. (EE)
Due to radar's range measurement accuracy, Range Time plots are used to represent radar data. When objects' tracks cross on a Range Time plot, it is uncertain which track belongs to which target. An analysis of the frequency and angle of these crossings was performed. Mathematical analysis concluded that in certain situations, only one type of crossing can result. Further Monte Carlo simulations were used to study these crossing statistics in other situations.
In addition, it was examined how well targets could be tracked through an individual crossing. The probabilities of correct track association were calculated as a function of a variety of factors. Given our models and assumptions, sensor fusion of Range Time and Range Doppler analysis substantially improved crossing classification.
Evaluation Bench for Portfolio Optimization
Student:
Holban, Emilia D.
Advisor:
VERMES, D. (MA)
This project implements a MATLAB based evaluation workbench to assess and compare portfolio management strategies. Daily data for 170 stocks carefully selected to cover the market between Dec 24 1998 and March 31, 2008 forms the basis of the evaluation. Quarterly or yearly rebalancing is implemented. Three strategies are compared in the current implementation -- uniform, top quartile and optimized, minimum variance portfolios.
Group Theory in Chemistry
Student:
Johnson, Chase R.
Advisor:
SERVATIOUS, B. (MA)
This MQP examines the teaching practices concerning group theory in chemistry and chemistry in group theory at WPI as well as other colleges. The influence and importance of the interaction of the two subjects on each other is exemplified by its prevalence in academic texts as well as a recent research article in the mathematical sciences with applications in chemistry and a recent chemistry experiment, whose analysis used group theory as a tool.
Insurance Product Development
Students:
Copp, Jessica
Yurong, Mao Y.
Tolivaisa, Alexander
Advisor:
ABRAHAM, JON P. (MA)
The project's objective was to develop and price a new insurance product. Rollercoaster insurance was chosen for its uniqueness. Data for injury numbers, number of riders and deaths were necessary for pricing, but primarily private. Risk rate and ridership were modeled based on limited parks' data. A portfolio was developed using the modeled data. The purpose of portfolios was to share the risk and reduce premiums. After adding in expense and profit, a final premium was determined for each rollercoaster.
Cracks in Half Plane, Cracks in Discs
Student:
Owens, William R.
Advisor:
VOLKOV, D. (MA)
This project starts from an eigenvalue problem of Steklov type which models displacement fields occurring during the destabilization of faults in elastic media. We introduce and study in details the functional space V, a generalized solution space for this eigenvalue problem. The original formulation valid for half planes is then extended to problems in disks by conformal mapping.
Examination of Gravity Waves over Toppography Using Long's Equation
Student:
Simpson, Maxwell T.
Advisor:
HUMI, M. (MA)
This project models the behavior of steady gravity waves in the atmosphere over terrain using Long's Equation. We examine the derivation and assumptions behind the equation and determine how its solution depends on its parameters and the height of the terrain. We solved the equation both analytically using perturbation methods and numerically using the finite difference method with a sponge layer to prevent unrealistic wave reflection at the boundary.
The Great Lakes Insurance Company
Students:
Brokaw, Jeremey Johnathan
Shen, Karl
Yin, Zijing
Advisor:
ABRAHAM, JON P. (MA)
This project researches the process an insurance company goes through to price boat insurance. Gathering data from boating statistics and insurance companies, a simulation product is created, utilizing accident rates, expected losses, and operator characteristics. This new product offers personal property, liability, and medical protection; as well as a unique policy for death benefits. Assuming realistic conditions like regional factors, business expenses, and projected customer base; the resulting insurance policy is both profitable and competitive in real life situations.
Sampling Strategies for Error Rate Estimation and Quality Control
Students:
Facchiano, Nicholas John
Kingman, Ashley L.
Olore, Amanda B.
Zuniga, David Eduardo
Advisor:
ABRAHAM, JON P. (MA)
WILBUR, J. D. (MAC)
John Hancock must utilize processes to monitor departmental performance. Our group was presented with several problems whose solutions will benefit the company's quality assurance capabilities. This MQP analyzes the optimization of a sampling function for a book of insurance policies, the bootstrapping method for the estimation of policy shortfall confidence intervals, and a sampling procedure to aid the company in customer satisfaction screening.
Financial Computations on the GPU
Students:
Yamshchikov, Andrey Andreyevich
Zhao, Shengshi.
Advisor:
ABRAHAM, JON P. (MA)
AGU, E. O. (CS)
This Major Qualifying Project investigates the performance benefits of using the Graphics Processing Unit for algorithmic trading. The accomplished work includes the design, development and rigorous testing of a financial application to analyze real-time market data. Comprehensive analysis and an elaborate discussion of the results show that the GPU outperforms the CPU by several factors.
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Last modified: November 20, 2008 14:37:05