The Valuation of Joint Life and Survivorship Annuities

Abstract

Joint life and survivorship annuities on two lives form a troublesome class to deal with in valuations. Since the reserves are functions of two variables the annuities fall naturally into so many groups that they are often valued individually. In an office which writes much annuity business this process is laborious.

A unitised fund approach to with-profit business

“…4 The modern solution to this problem is to credit the whole of the net premium to the unit account in the first instance and then cancel a number of units each year to pay for the life cover. No doubt the actuaries who designed these contracts will have retired before the policyholders start writing in to enquire why the number of units cancelled is greater than the number credited.…”

“…4 We realised that the day would come when this simple conclusion would be insufficient and that we would need a mechanism for determining what further guidance the investment managers should be given. There are two risks that we have to consider.…”

“…4 The problem with pricing the units to include credit for a potential tax rebate in respect of a capital loss is that it will only be of value as an offset against A Unitised Fund Approach to With-Profit Business 293 subsequent capital gains, and we cannot be sure that these will occur. For this reason, we believe that the normal practice in pricing units of internal funds used for linked policies is not to allow any credit for capital losses.…”

“…4 shows the all equity portfolio as in Table 8.1. The unit price in year 2 of 97.17p is slightly higher than the corresponding 'critical value' in Table 8.1 as a result of the higher dividend assumed.…”