Annuities with controlled random interest rates

Abstract

We derive the expected values of annuities with random interest rates modeled by a reflected Brownian motion with a switchover at some positive level at which the drift and variance parameters change. The lifetime of the annuity is assumed to be exponentially distributed. The approach can be extended to the case of several switchover levels. We also consider other related models. (C) 2003 Elsevier Science B.V. All rights reserved.