# 1998-99 Projects

ODEToolkit is a mathematical software module used to solve systems of first-order ordinary differential equations (ODEs) or single equations of first or second order. ODEToolkit is written in JAVA, a platform independent programming language that is ideal for developing programs to be used across the World Wide Web. ODEToolkit uses a set of powerful solving routines written in FORTRAN called ODEPACK to solve ODEs.

### Dangers of Diversification

Students: Jessica A. Buffone, Michael F. Bugbee

There exists no single measure of risk that is appropriate to all investors, partly because there is no clear definition of risk. Investment strategies such as diversification are often used in an attempt to reduce risk. We analyze several risk and performance measures and discuss their implications for investors with various risk preferences. We then determine the correlation between these risk and performance measures to illustrate their similarities and differences. This project was done in cooperation with Aetna Retirement Services.

### An Assessment of MCI's Proactive Program at Charlton, MA

Student: Samuel T. Lehane-Abraham

This project compares the efficiency of MCI's circuit repair proactive program in Charlton with all other MCI terminal sites across the country. Preliminary analyses show that MCI at Charlton performs similar, yet slightly worse than the other terminal sites combined. Both non-spatial and spatial (communication among sites) models are used to make inference. With respect to circuit repair time Charlton is better than a few and worse than a few, but on average was similar to the other terminal sites.

### Inflationary Effects on Loss Reserves

Student: Melissa A. Garrell and Karen M. Lee

Accurate reserves for future claims are crucial to the financial success of an insurance company. This project compares the reserving model currently used by Travelers Property & Casualty (retrospective in nature) to a model suggested by Robert Butsic (prospective, allowing for changing inflationary trends). A common mathematical language for the two models is developed, an Excel program to implement them is written, and numerical simulations run to make comparisons.

### Finite Element Simulations in Plasticity

Student: Xiao-Long Yu

The project's goal is to provide a user-friendly, web-based system for solving practical matching problems. Users are not expected to have any specialized training. The matching engine takes care of interpreting user input and applying appropriate algorithms. This report focuses on the theoretical foundations of the matching engine.

### Pricing Guaranteed Variable Life Insurance

Student: Aaron Korthas and Shelby Woods

By simulating hypothetical Medallion Variable Life Insurance policies, appropriate premiums are determined to guarantee a death benefit for various lengths of time under various investment scenarios. With these premiums there is an estimated high probability of having an adequate account balance by the end of the guarantee periods. As with any guarantee, John Hancock will lose money on policies that fail. Additional fees are calculated to offset the expected losses of failed policies.