Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

8-2001

Committee Chair or Co-Chairs

Don Hong

Committee Members

James Boland, Robert M. Price Jr.

Abstract

We begin by examining the accumulated value functions of some annuities-certain. We then investigate the accumulated value of these annuities where the interest is a random variable under some restrictions. Calculations are derived for the expected value and the variance of these accumulated values and present values. In particular we will examine an annuity-due of k yearly payments of 1. Then we will consider an increasing annuity-due of k yearly payments of 1, 2, ⋯ , k. And finally, we examine a decreasing annuity-due of k yearly payments of n, n - 1, ⋯ , n - k + 1, for kn.

Finally we extend our analysis to include a contingent annuity. That is an annuity in which each payment is contingent on the continuance of a given status. Specifically, we examine a life annuity under which each payment is contingent on the survival of one or more specified persons. We extend our methods from the previous sections to derive the formula of the expected value for the present value of the life annuities of a future life time at a random rate of interest.

Document Type

Thesis - Open Access

Copyright

Copyright by the authors.

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