William Morgan's yearly computation of expected deaths and of accounts showing the state of the Society 1768-1827
Yearly computation of expected deaths and of accounts showing the state of the Society, 1768-1827, made by William Morgan according to the plan suggested by Richard Price.
The Society for Equitable Assurances first designated the title 'actuary' in its deed of settlement of 1762 to fulfil a lead administrative function in presenting applications for life assurance to the Court of Directors. William Morgan (1750-1833) was engaged as Assistant Actuary to the Society for Equitable Assurances on the recommendation of his uncle Richard Price in 1774. A year later he became the Actuary and served from 1775 to 1830, developing the mathematical role as the modern actuary we know today.
William Morgan's work dominates the Archive of the early period and the archives held at Staple Inn library. Among others, this manuscript work compiles the tabulated mortality experience of policyholders and presenting the summaries of the Society's accounts year by year from 1768 to 1827 is a special example. Morgan followed the instruction of Price in conducting the first actuarial valuation of policies in 1776 to determine the Society's financial position to meet claims over the long term. The appraisal identified a 'surplus' (profit) for the Society whereby premium income would exceed expected levels of claims (based on mortality projections). This allowed the Society to consider return to members: revised lower premiums (from improved mortality assumptions), an interim 'bonus' return to policyholders or a higher reversionary payout to claimants. A cautious actuarial approach also looked to recommend that some surplus was retained to be ready for seasons of higher mortality in the future.
In earlier tables shown in the work, there is comparison of the Society's policyholders' mortality experience up to 1788 with that proposed in Dodson's Tables (of 1756) and that shown by Edmund Halley (in his paper to the Royal Society in 1693) but from 1788 comparison too is made with the experience of the Northampton which Richard Price had signalled as a source in Observations on Reversionary Payments (editions from 1771 but especially from 1783) and which William Morgan would update from the fifth edition of 1792 after Price's death.
Morgan's research informed his publications the Doctrine of Annuities and Assurances on Lives and Survivorships stated and explained (1779) and The Principles and Doctrines of Assurances, Annuities on Lives, and Contingent Reversions (1821) and his manuscript work has been celebrated in articles by the Society's actuary in the early twentieth century, William Palin Elderton.