## Research Experiences For Undergraduates (REU)

# REU 2004 Projects

## Numerical Models for Tumor Growth

Sponsor: IBM Corporation

Advisor: Prof. Suzanne L. Weekes

Erica Johnson | Christopher Long | Brian Skjerven | Kimberly Ware |

Currently, a person diagnosed with glioblastoma (GBM), a highly invasive cancer of the structural cells in the brain, has an extremely low chance of long-term survival. One of the obstacles in treating GBM is the inability of current medical imaging technology to observe growth at an extremely small scale. Our task, in cooperation with IBM Corporation and researchers at Harvard University, is to develop a continuum model that accounts for both the proliferation and migration of tumor cells. In formulating this model, we will use a system of partial differential equations to describe the dynamics of the tumor and its effects on the surrounding brain tissue. In addition, we will employ finite difference methods to approximate the solution to the system. Our goal is to utilize our model in understanding patterns and initial stages of tumor growth.

## Volatility Costs for an Assigned Risk Plan

Sponsor: Premier Insurance

Advisor: Prof. Arthur C. Heinricher

Dustin Chase | Suzanne Ferrell-Locke | Kimberly Millard |

The Massachusetts private passenger automobile insurance market is in poor condition. Thirty-four of the fifty-three companies that wrote insurance in the state in 1990 have left the state since then, while only three have entered. Of the 34 that left, 30 paid a large 'buy out' fee to leave the state. The reasons for this situation are complex, but they can broadly be explained by the market structure Massachusetts uses to handle high risk drivers. Over the next few years, a new market structure for handling these risks will be implemented. Our task is to model this new structure.

## Alternate Methods for Covariance Estimation in Portfolio Analysis

Sponsor: New Frontiers Advisors

Advisor: Prof. Carlos Morales

Ruth Griswold | Andrew Magyar | John Penuel | Jessica Scheld | Jean Wilsher |

With the support of New Frontier Advisors, our group at WPI is working on a problem within the finance world; to optimize returns while minimizing risk, as measured by the asset covariance matrix. The ultimate goal would be to find the true covariance matrix, from which the efficient frontier can be derived. However, since the true covariance matrix is impossible to completely determine, several models have been proposed to estimate it. Unfortunately, no single model estimates the covariance matrix in a superior way. Thus, we will combine models in order to minimize the error involved within the final model. From this new covariance matrix, we can come up with an efficient frontier which represents the portfolios which will yield optimal points of return versusrisk.

Maintained by webmaster@wpi.eduLast modified: Jun 20, 2010, 22:58 EDT