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The Actuary The magazine of the Institute & Faculty of Actuaries
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The Greatest British Actuary Ever

The mention of Frank Redington and his theory of ‘immunisation’ in the July issue (p18) made me wonder if anyone else has ever noticed that the proof of this theory that he set out in his 1952 paper is fallacious.

Redington employed Taylor’s theorem to prove his contention that it was possible to dispose the assets of a life fund in such a way that any movement in interest rates, upwards or downwards, would result in a gain against the value of the liabilities. Taylor’s theorem states that if the value of a function and all of its derivatives are known at a single point, the value of the function at any point can be determined. Redington used the premise that the asset and liability values were functions of the rate of interest and then employed Taylor’s theorem to demonstrate that it might be possible to ensure that the value of the difference at any point was always positive.

The problem with this is that Taylor’s theorem requires that the function and all of its derivatives must be continuous, that is to say no breaks and sharp corners in the graph of the function itself and all its derivatives, but it is obvious that movements in interest rates are discrete rather than continuous so that I have always been of the opinion that it is fairly obvious that employing Taylor’s theorem in this context does actually not prove anything at all.