# REU 1998 Projects

## Optimal Cession Strategies

 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

 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

 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.