Life Annuities under Random Rates of Interest.

<p>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 <em>k</em> yearly payments of 1. Then we will consider an increasing annuity-due of <em>k</em> yearly payments of 1, 2, ⋯ , <em>k</em>. And finally, we examine a decreasing annuity-due of <em>k</em> yearly payments of <em>n</em>, <em>n</em> - 1, ⋯ , <em>n</em> - <em>k</em> + 1, for <em>k</em> ≤ <em>n</em>.</p> <p>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.</p>

Name thesis:degree_name

MS (Master of Science)

Level thesis:degree_level

Thesis - unrestricted

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.issued

2001

Author dc:creator

• Baker, Lesley J.

• Life Annuities
• Random Interest Rates
• Annuities
• Physical Sciences and Mathematics

Statement dc:rights

• Copyright by the authors.

Repository record dc:identifier

https://dc.etsu.edu/etd/135

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-1185