Estimating actuarial present value factors for annuity business using a non-parametric graduation approach
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Date
2019-06
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Publisher
KNUST
Abstract
Abstract
Ensuring income security after retirement has been an issue troubling many
countries. Over the years, several attempts have been made to improve upon
pensions of retirees. A typical example is the introduction of the new pension
scheme in Ghana. Yet, pensioners are still faced with the problem of nding an
investment with a guaranteed payout for their pensions. To this end, the use of
life annuities is proposed as a solution since life annuities have been touted to
ensure a guaranteed payout. However, it is unfortunate to note that not only does
Ghana lack a ready annuity market, the country also does not have a standard
mortality table to undertake such annuity operations.
Hence, in this study, the modi ed actuarial exposure method was applied
to a pension scheme data in Ghana to estimate the crude mortality rates.
The Whittaker-Henderson and the modi ed Whittaker-Henderson graduation
methods were then applied to the estimated crude mortality rates to achieve a
smooth and increasing progression of mortality rates with age. The Generalized
Cross-Validation (GCV) method was then applied to obtain a suitable smoothing
parameter, h at each order of di erencing, z that minimized the GCV score. The
optimal set of graduated mortality rates with desirable features was produced by
the Whittaker-Henderson method at z = 3 and h = 100. The selected graduated
mortality rates were further used to compute life expectancy. Finally, annuity
tables were developed from the estimated Actuarial Present Value (APV) factors
to be used in pricing the annuity products.
Description
A thesis submitted to the department of mathematics in partial fulfilment of the requirements for the Degree of Doctor of Philosophy in Actuarial Science College of Science