The technique described by Miss Merriman in the preceding note can be applied, with suitable alterations, to many different types of life assurance and annuity funds as well as to pension funds. By the use of approximate methods it is possible to abbreviate the working within a comparatively small compass, whilst retaining sufficient accuracy to afford a guide for investment policy. This note describes a particular application of these methods.

The Management Committee of a large Widows' and Orphans' Fund sought the Actuary's advice on the probable future progress of the Fund. The Fund was established many years ago, but the membership has been expanding and both contributions and benefits have been increased from time to time. It was clear on general grounds that, if sufficient new entrants were admitted to maintain the present membership without limit of time, financial maturity would not be reached for many years. On these assumptions the Fund would eventually reach stability, but it would never decrease, so that from this point of view irredeemable investments could be purchased in the belief that they would never have to be sold. The adoption of this theory, however, would be tantamount to making the future surplus or deficiency of the Fund in some way contingent upon the future flow of new entrants.