SummaryThe paper concerns the situation in which an evaluation of outstanding claims is discounted, in anticipation of investment return earned by the funds supporting that liability. Factors bearing upon the choice of an appropriate rate of return to be assumed in this evaluation are considered.The ‘standard approach’ to this problem is criticized in two main respects:(i) there is usually no statement (indeed, no consideration) of whether the discounted value of outstanding claims is to be associated with assets at book, market, or some other value;(ii) the discounting of outstanding claims is often performed by means of an assumed ‘inflation gap’, i.e. an assumed difference between future rates of inflation and investment return.Various other matters germane to the determination of an appropriate rate of investment return are listed in Section 2.Sections 3 and 5 deal particularly with points (i) and (ii) raised above. It is suggested that, in certain circumstances, an evaluation of outstanding claims which fails to address (i) or is carried out on an ‘inflation gap’ basis will be virtually meaningless.Section 4 deals with the case of an insurance fund in which assets are matched with technical liabilities by amount and term. The considerations which would cause the rate of investment return projected in these circumstances, to differ from that projected in the case of an absence of matching are discussed.Section 6 deals with the issue of exactly which assets are to be regarded as supporting the liability for outstanding claims. It is apparent that the identification of such assets will affect the rate of return to be regarded as referable to outstanding claims. Particular matters considered include:(i) assets to be associated with acquisition of new business (and hence not with outstanding claims);(ii) debtor and creditor items. particularly outstanding premiums and inwards loans.Section 7 gives a numerical example of the projection of future rates of investment return. This is done by means of a computer projection of various items of a hypothetical insurance fund, taking into account projected future:(i) interest rates;(ii) rate of growth of new premium;(iii) the required distribution of assets by sector;(iv) profitability of business underwritten.Conclusions on the various matters considered are dotted through the paper. For convenience, they are collected together in Section 8.
Logarithmic stability in determination of a 3D viscoelastic coefficient and a numerical example
