# REU 2005 Projects

## FEMLAB Electromagnetic-Thermal Model of Microwave Thermal Processing

 Christopher Mirabito Anu Narayanan David Perez Brenton Stone

In a microwave oven, food is heated as a result of two simultaneous physical processes: absorption of electromagnetic energy (as a result of the transmission of electromagnetic waves), and heat diffusion. It is known from experience that microwave heating can often be very non-uniform and hard to control. A system of coupled partial differential equations modeling these two phenomena is formulated but it is impossible to solve exactly except in trivial cases. We investigate the use of the finite element method software FEMLAB in obtaining numerical solutions to our coupled system. We hope our model aids in designing microwave ovens which have more control over how food is heated.

## Portfolio Optimization with Non-Smooth Constraints

 William Bade Jessica Clark Alex Mills

This project develops a portfolio optimization algorithm tailored to the special structure provided by constraints on the sum of the absolute values of the positions; a book size constraint. The program generates the efficient frontier by scanning for corner portfolios, using the fact that optimal portfolios must satisfy a combination of equations (for each stock which is not zero) and inclusions (for each stock that is not in the solution).

## Estimating the Cost of Extending a Term Insurance Policy

Sponsor: John Hancock Life Insurance Company
Advisor: Prof. Jayson Wilbur, Prof. Andrew Swift, Prof. Jon Abraham

 Nathanial Burch Sarah Hartenstein Razvan Ionescu Eugene Quan

A term life insurance policy pays out a death benefit to its beneficiary provided that the insured individual dies within the term of the policy.. There are situations in which the insurance company may wish to extend the length of the term life insurance policy. Since such a contract extension increases the length of time that the individual is insured, there is an associated cost to the company. The focus of this project, proposed by John Hancock Life Insurance Company, is to use various mathematical and statistical tools to estimate this cost. The final product includes a Microsoft Visual Basic for Applications software tool, which actuaries at John Hancock can use to estimate the cost of extending any given term life insurance policy.

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