## Research Experiences For Undergraduates (REU)

# REU 1998 Projects

## Optimal Cession Strategies

Sponsor: Premier Insurance

Advisor: Arthur Heinricher

Kristin Blenk | Jesse Field |

In Massachusetts, auto insurance rates are set by the state and no company can refuse to insure any customer who walks into its offices. On the other hand, the companies do have the option to "cede" policies that they believe are too risky to a state agency called CAR (Commonwealth Automobile Re-insurers). When a policy is ceded, most of the premium, and all of the losses, are passed on to CAR.

The problem then is to decide who to keep and who to cede and the objective is to maximize the company's final profit.

The twist in the problem is that ceding policies is not free. A company pays CAR an amount at the end of the year which depends on not only how many vehicles the company ceded, but also on the cession behavior of the rest of the companies in the state for that year.

The REU project focuses on the statistical aspects of the prediction problem.

## Design of a Bending Pipe

Sponsor: Morgan Construction

Advisor: Bogdan Vernescu

Jon Kennedy | Peter Trautman |

In a rolling steel mill, blocks of red-hot steel are run between rollers
until the blocks are stretched into long thin rods. At the end of the production
line, these rods are traveling at close to 250 mph and you (or the steel
manufacturer) has about 5 feet to stop the rod. Engineers (many years ago)
designed an ingenious method for solving the problem: the pipe is sent into a *bending
pipe* (shaped like a piece of a cork screw) and the linear motion is
converted into rotational motion.

A well-designed pipe would be cheap to make and last as long as possible. The life of the bending pipe is related to the rate of wearing inside the pipe (which depends on the path of the steel rod against the wall of the pipe and the force that the rod exerts on the wall).

The project focuses on a combination of problems. First the accurate description of the path followed by the steel rod inside the pipe, and second the modeling the wear for a particular pipe design.

## Estimating Success Probabilities of Variable Life Insurance via Simulation

Sponsor: John Hancock Insurance

Advisor: Ann Wiedie

Jonathan Van Haste | Heather Stultz |

In a variable life insurance policy a portion of the premium is invested in
the market, and due to the variability inherent in the market the value of the
policy is random. Previously, a *deterministic* perspective had been used
to explain behavior of the policy; if the market has a fixed annual rate of
return of *p* percent, then *n* payments are required to fully fund
the policy and *a*(*t*) will be the value of the policy at time *t*.
This narrow view can be misleading to policyholders, since such consistent
behavior is rarely exhibited by the market. The project involves describing the
behavior of the policy in a *probabilistic* manner, by simulating the
behavior of the market under various conditions and computing the resulting
effects on the policy, and estimation of the distributions of the number of
premium payments required to fund a policy and the accumulated value of the
policy at a particular time.

In particular, the summer REU refined a previously written computer program to accurately compute policy behavior (determining fees, charges, and credits correctly.) Then, the team used this program to estimate the probability of success (the account achieving at least the death benefit by age 100) under various premium amounts and market behavior parameters. The results were somewhat unexpected and of great interest to the sponsor! Finally, suggestions were provided regarding an educational program for teaching salespeople about the behavior of this product.

## Optimal Control of HVAC Systems

Sponsor: UTRC

Advisors: Arthur Heinricher and Bogdan Vernescu

Ane Coughlin | Dwayne Ellington | Brian Rieksts | Ellen Phifer |

HVAC systems represent a large percentage of the operational cost of a building, and control many aspects of the building environment including: heating, cooling, air quality, and humidity. The behavior of HVAC systems can be simulated using an ODE model based on simple Thermodynamical processes.

The goal of this REU project is to formulate and solve the Control Optimization problem which finds the correct operating parameters which minimizes the operational cost of an HVAC system over a whole year while meeting the criteria set for the building environment.

Maintained by webmaster@wpi.eduLast modified: Jun 20, 2010, 15:24 EDT