Abstract: Banks lend money to consumers. One of such types of loans is home mortgage. These loans have the underlying house (property) as collateral, and often the terms of the loans are very long: 10, 15 or 30 years.
Student Researchers: Michael Driscoll and Will Abbott
Advisors: Thorsten Moening, Heekyung Youn
Abstract: In recent years, variable annuity products have become a popular investment vehicle, in part due to their favorable tax treatment. A policyholder of a variable annuity often directs the insurer to invest his/her money in the equity market and hence faces an uncertainty that the investment might lose value. To offset this risk, at least partially, the policyholder can purchase (for an additional fee) a guarantee such as a Guaranteed Minimum Death Benefit (GMDB) that guarantees a certain level of payout at the time of the policy holder’s death if that happens before the policy maturity. Similarly, a Guaranteed Minimum Accumulation Benefit (GMAB) ensures that the policyholder will be paid a certain minimum amount at maturity if the policy holder survives till then, even if the fund value drops below the minimum level. In this project, we will investigate whether the fees charged by the insurance companies reflect the benefits provided. In particular, we want to consider whether the fee should depend on the policyholder’s age at inception of the variable annuity, and to what extent insurers account for that in practice.
Student Researchers: Michael Painter and Dane Schreiber
Abstract: Hyundai cars carry 100,000 miles/10 year warranty. Repair records of the cars are closely tracked in terms of types of repair and the times of repair. We will study joint distributions of lifetimes of different vehicle components. In particular, we will single out a principal component, and try to see if the other components’ failures may trigger the failure of the principal component.
The project will utilize linear and non-linear regression, copula modeling, and possibly Markov Chain Monte Carlo methods to help predict future failures of the principal component.
Student Researchers: Jake Damiani and Stephanie Fritz
Advisor: Magdalena Stolarska
Abstract: Craniosynostosis is a condition in infants where skull plates fuse prematurely leading to abnormal skull and brain growth. Due to the fact that abnormal brain growth can increase intracranial pressures, which can have adverse affects on development, the aim of this project is to develop a model and run simulations of the growing brain/skull system and quantify the intracranial pressures that occur when particular skull plates are fused. To develop the model, students will use mathematical methods based on continuum mechanics and use the finite element method for simulations.
Student Researchers: Jackson Penning and Madeline Anderson
Advisor: Doug Dokken
Abstract: Students will need to familiarize ourselves with the visualization software “VisIt” as well as CM1 on Linux and Unix operating systems. Then we will collect data on the weather of past tornadoes in order to generate a tornado on in the computer simulated storm. We will analyze this data to determine exactly why some storms result in tornadoes and why others do not.
Student Researchers: Alexander Bates, Zachary Boyle, Charlie Pechous, and Alexandra Ubel
Advisor: Lisa Rezac
Abstract: This project will examine the importance of radian measure in mathematics, a practical application of radian measure in use today, and activities that will help students understand radian measure more deeply.
Studnet Researchers: Michael Driscoll and Will Abbott.
- Search “Mathematics Teacher” Journal and related resources (NCMT Illuminations) for Radian Measure Activities, and historical explanations and uses of radian measure
- Examine the practical application of Radian measure in military mapping
- Compare and contrast the introduction of radian measure in typical textbooks
- Produce an “Illuminations”- type lesson plan or “Mathematics Teacher”- type article summarizing work and incorporating practical applications of radian measure.
Abstract: Reverse mortgages (RMs) are experiencing a resurgence as the U.S. economic recovery becomes more evident. The aims of this project include the following parts:
- understanding the terms of a typical RM
- recognizing the risks and rewards of a RM from the point of view of each of the three primary participants: the lender, the borrower and the insurer
- modeling housing values
- modeling RM termination probabilities
- modeling the financial risks and rewards for the RM participants
- seeking to identify optimal termination strategies for the borrower and the related impact on insurers
- identifying, if possible, hedging strategies for the insurer
Studnet Researcher: Jake Damiani
Advisor: Paul Ohmann
Abstract: The Selfish Herd Hypothesis asserts that certain animals congregate because of the protective quality that this grouping confers – i.e. individuals are less exposed to predators. This is often modeled by defining a “degree of danger” around each individual and showing that clumping together helps minimize this value. Typically, these simulations start with a sizable collection of individuals, but what happens when the density of individuals is sparse? Can we determine when it is in the best interest of individuals to congregate when there isn’t already a sizable group to follow? Is there a tipping point beyond which groupings will tend to be large, and below which groupings are either disfavored or else otherwise constrained to be small? This project will attempt to investigate these questions.
Student Researcher: Nick Ose
- Background reading and synthesis of the historical papers on this subject (e.g. Hamilton, W.D. (1971), “Geometry for the Selfish Herd”, Journal of Theoretical Biology 31:295-311.)
- Build Matlab predator-prey models with various small numbers of prey. We will need to define and keep track of relevant quantities, such as prey lifetimes and distances between individuals. We will also need to carefully analyze these simulations in order to interpret the results.
- Write a final report summarizing the project, following CAM’s guidelines for final reports.
- Present your results at the Inquiry at UST Poster Session in September.
Abstract: Ruled surfaces have been used by famous architects throughout the ages, such as Gaudi in his masterpiece, La Sagrada Familia. As another example, the Vatican has several impressive ruled surfaces that St. Thomas students have seen in a J-Term course that focused on geometry and mechanics of architecture. The student researchers will learn about the mathematical theory of ruled surfaces and using appropriate software, will create files of well-known geometrical structures that are printed out in plastic on a 3D printer, also known as rapid prototyping in mechanical engineering.
Research Description: Focus is on two fundamentally different approaches based on either using Mathematica or MATLAB (and/or SolidWorks). For the Mathematica approach, there are several steps envisioned, specifically: (a) characterizing the ruled surface mathematically with the appropriate equations, (b) either creating a so-called STL file that can be input directly to a rapid prototyping machine or employing SolidWorks to further process the numerical surface data from which the STL file can be created. In the case of the MATLAB approach, given the fundamental surface equations, there are 3 different ideas on how best to create ruled surface part models: (a) create surfaces in MATLAB using specialty commands and then proceeding on to SolidWorks if necessary and the 3D printer, (b) exporting coordinate data, such as for grid points, to SolidWorks, and then using surface tools to further process prior to generating the printable STL file, and (c) just use SolidWorks directly to create the model. We have several specific surfaces that we would like to have modeled. Upon completion, we will evaluate the capabilities and tradeoffs associated with each approach.
Student Researchers: Mitchel Arves and Jon Erickson