Function space integration for annuities

We derive explicit formulas for the expected values of annuities with a ran dom interest rate, modeled by a reflected Brownian motion at zero (RBM) sto pped by certain Markov times. We consider times tau of the following kinds: (i) tau is constant, (ii) tau is a random and independent of the RBM X, (i ii) tau is the first time X reaches a prespecified level, and (iv) minima o f these stopping times. The case of Brownian motion without reflection is a lso briefly discussed. (C) 2001 Elsevier Science B.V All rights reserved.