Hello,

I have a question about this concept from Mahler:

"The computation of the EPV for severity is similar to that for frequency with one important difference. One has to weight together the process variances of the severities for the individual types using the chance that a claim came from each type. The chance that a claim came from an individual of a givent ype is proportional to the product of the a priori chance of an insured being of that type and the mean frequency for that type. Taking into account the mean frequencies in this manner is only necessary when one is predicting future severities and the type of insured includes specifying both frequency and severity.:

For die/spinner models we don't need to do this because the die for frequency and spinner for severity are chosen independently and thus frequency and severit are not specified.

I encountered this problem involving continuous risk types.

Losses for individual policyholders follow a Compound Poisson Distribution. The prior distribution of the Poisson parameter lambda is uniform on [2,6]. Severity is Gamma with parameters alpha=3 and theta. Theta has an inverse gamma distribution. The distributions of lambda and theta are independent.

To me, this is a continuous analogue for a die/spinner model: picking a frequency distribution is independent of picking a gamma distribution. But what would happen if we said that severity is specified, say alpha = 3 and theta = 5 for every individual policyholder, but the Compound Poisson Distribution remains for picking frequencies? In a way, we are eliminating the spinner, but the die remains.

If we want to compute EPV and VHM for Buhlmann credibility estimation of future severity, what kind of weights do we assign to the hypothetical means and process variances of severity? Do we weight according to the frequency process, for example a priori chance of picking a lambda times mean frequency: 1/(6-2) * lambda, all divided by integral of 1/4 lambda, from 2 to 6?

Thanks

I have a question about this concept from Mahler:

"The computation of the EPV for severity is similar to that for frequency with one important difference. One has to weight together the process variances of the severities for the individual types using the chance that a claim came from each type. The chance that a claim came from an individual of a givent ype is proportional to the product of the a priori chance of an insured being of that type and the mean frequency for that type. Taking into account the mean frequencies in this manner is only necessary when one is predicting future severities and the type of insured includes specifying both frequency and severity.:

For die/spinner models we don't need to do this because the die for frequency and spinner for severity are chosen independently and thus frequency and severit are not specified.

I encountered this problem involving continuous risk types.

Losses for individual policyholders follow a Compound Poisson Distribution. The prior distribution of the Poisson parameter lambda is uniform on [2,6]. Severity is Gamma with parameters alpha=3 and theta. Theta has an inverse gamma distribution. The distributions of lambda and theta are independent.

To me, this is a continuous analogue for a die/spinner model: picking a frequency distribution is independent of picking a gamma distribution. But what would happen if we said that severity is specified, say alpha = 3 and theta = 5 for every individual policyholder, but the Compound Poisson Distribution remains for picking frequencies? In a way, we are eliminating the spinner, but the die remains.

If we want to compute EPV and VHM for Buhlmann credibility estimation of future severity, what kind of weights do we assign to the hypothetical means and process variances of severity? Do we weight according to the frequency process, for example a priori chance of picking a lambda times mean frequency: 1/(6-2) * lambda, all divided by integral of 1/4 lambda, from 2 to 6?

Thanks