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.