Function space integration for annuities

Abstract

We derive explicit formulas for the expected values of annuities with a random interest rate, modeled by a reflected Brownian motion at zero (RBM) stopped by certain Markov times. We consider times τ of the following kinds: (i) τ is constant, (ii) τ is a random and independent of the RBM X, (iii) τ is the first time X reaches a prespecified level, and (iv) minima of these stopping times. The case of Brownian motion without reflection is also briefly discussed.