Loss Models: From Data to Decisions, 4th Edition

17.5 Problems with the approach

While the limited fluctuation approach yields simple solutions to the problem, there are theoretical difficulties. First, there is no underlying theoretical model for the distribution of the X_js and, thus, no reason why a premium of the form (17.7) is appropriate and preferable to M. Why not just estimate ξ from a collection of homogeneous policyholders and charge all policyholders the same rate? While there is a practical reason for using (17.7), no model has been presented to suggest that this formula may be appropriate. Consequently, the choice of Z (and hence P_c) is completely arbitrary.

Second, even if (17.7) were appropriate for a particular model, there is no guidance for the selection of r and p.

Finally, the limited fluctuation approach does not examine the difference between ξ and M. When (17.7) is employed, we are essentially stating that the value of M is accurate as a representation of the expected value given no information about this particular policyholder. However, it is usually the case that M is also an estimate and, therefore, unreliable in itself. The correct credibility question should be “how much more reliable is compared to M?” and not “how reliable is ?”

In the next chapter, a systematic modeling approach is presented for the ...