New Econ for Life Actuaries

In an editorial in ASTIN BULLETIN, Hans Bühlmann (2002) suggests it is time to change the teaching of life insurance theory towards the real life challenges of that industry. The following note is a response to this editorial. In Bergen we have partially taught the NUMAT, or the NUMeraire based Actuarial Teaching since the beginning of the 90ties at the Norwegian School of Economics and Business Administration (NHH). In this short note we point out that there may be some practical problems when these principles are to be implemented. Actuarial Mathematics vs Financial Economics As recognized by Bühlmann the model used in Life Insurance Mathematics is built on the two elements: (i) mortality, and (ii) time value of money. This is, however, not sufficient to comprise a consistent pricing theory of a financial product, such as a private life insurance contract, a pension or an annuity. It is rather remarkable that mathematicians have, for more that 200 years, arrogantly (or more precisely, ignorantly) disregarded any economic principles in pricing such products (or any other insurance products for that matter). It should not come as a surprise that it is rather natural to use the economic theory of contracts to study insurance contracts. Financial pricing of life insurance contracts often starts by assuming the existence of a market of zero coupon bonds. The market price at time zero B0(t) of a default free unit discount bond maturing at the future time t is typically given by the formula B0(t) = E Q{e− R t 0 r(s) }, (1)