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.
Original language | English |
---|---|
Pages (from-to) | 73-82 |
Number of pages | 10 |
Journal | Insurance: Mathematics and Economics |
Volume | 29 |
Issue number | 1 |
DOIs | |
State | Published - 20 Aug 2001 |
Keywords
- Annuity
- Markov time
- Random interest rate
- Reflected Brownian motion
ASJC Scopus subject areas
- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty