On annuities under random rates of interest

Abstract

In the article we consider accumulated values of annuities-certain with yearly payments with independent random interest rates. We focus on general annuities with payments varying in arithmetic and geometric progression which are important basic varying annuities (see Kellison, 1991). They are equivalent to the types studied recently by Zaks (2001). We derive, via recursive relationships, mean and variance formulae of the final values of the annuities. As a consequence, we obtain the moments related to the already discussed cases, which leads to a correction of main results from Zaks (2001).Finance mathematics; Annuity; Accumulated value; Random interest rate;