Flaws, approximations and uncertainties in the estimation of the exposed-to-risk
This research analyses the theoretical basis of exposed-to-risk estimation. It defends the conventional actuarial approach against criticisms raised by Hoem (1984), and, in so doing, examines in detail the development of the actuarial profession's estimation techniques. Maximum likelihood estimates are shown to be closely related to the estimates of decremental probabilities derived using the conventional actuarial approach. The correct treatment of deaths when estimating the initial exposed-to-risk is considered and contrasted with what is often used in practice. The relationship between the initial and central exposed-to-risk is considered for a single decrement, two decrements and for select rates. The implications of alternative assumptions and approximations are considered. Some inaccuracies in tuition material of the Faculty and Institute of Actuaries and articles written about exposed-to-risk are highlighted. Other problem areas, such as the bias of calculated rates and estimation under policy and calendar year rate intervals, are also considered.
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