The first part of the paper consists of a mathematical analysis of a method of ensuring solvency in an expanding life office investing only in first-class dated and irredeemable securities on the assumption that the market price structure of dated medium to long term securities may change only in such a way that at any time the gross redemption yield for any particular term to redemption will bear a constant ratio to the yield on irredeemables. This leads to a method of valuation of liabilities which is independent of any subjective estimate of the future rate of interest.

The second part of the paper suggests a possible use of this method of valuation in conjunction with the technique of Linear Programming as an aid to the management of a life assurance and annuity fund. This is illustrated by a worked example relating to investment policy, and applications to new business policy and “gearing” are discussed generally.