Function space integration for annuities. (Q1413284)

The authors 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. They consider times \(\tau\) of the following kinds: (i) \(\tau\) is constant, (ii) \(\tau\) is a random and independent variable of the RBM { X}, (iii) \(\tau\) 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.