Abstract: Actuaries traditionally model the asset-liability risk (or interest rate risk) by using immunization (Taylor's theorem) to examine stability of present value relationships on a balance sheet. We present a dual approach using Fourier analysis to examine the stability of on-going interest rate spreads over time in an income statement. Part I introduces Fourier analysis and convolutions and applies them to the future interest rate spreads implied by an idealized balance sheet. This suggests a completely new picture of the asset-liability risk. Part II explores a possible Fourier analysis of the external interest rate environment that sharpens this new picture of the asset-liability risk.

Biographical Information: Jim Bridgeman is associate professor of mathematics at the University of Connecticut where he directs the graduate programs in actuarial science and financial mathematics. He has a Yale master's degree, is a fellow of the Society of Actuaries and had a varied 29 year career in the insurance industry before joining UConn in 2001.