10.2 Point estimation

10.2.1 Introduction

Regardless of how a model is estimated, it is extremely unlikely that the estimated model will exactly match the true distribution. Ideally, we would like to be able to measure the error we will be making when using the estimated model. But doing so is clearly impossible! If we knew the amount of error we had made, we could adjust our estimate by that amount and then have no error at all. The best we can do is discover how much error is inherent in repeated use of the procedure, as opposed to how much error we made with our current estimate. Therefore, this section is about the quality of the ensemble of answers produced from the procedure, not about the quality of a particular answer.

This is a critical point with regard to actuarial practice. What is important is that an appropriate procedure be used, with everyone understanding that even the best procedure can lead to a poor result once the random future outcome has been revealed. This point is stated nicely in a Society of Actuaries principles draft [105, pp. 779–780] regarding the level of adequacy of a provision for a portfolio of life insurance risk obligations (i.e., the probability that the company will have enough money to meet its contractual obligations):

The indicated level of adequacy is prospective, but the actuarial model is generally validated against past experience. It is incorrect to conclude on the basis of subsequent experience that the actuarial assumptions were inappropriate ...

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