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Old 01-25-2018, 03:02 PM
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Default MLE estimators

This question is from Adapt C Review:
Maximum Likelihood Estimators - Example 1
You are given:
i. Policy A has a policy limit of 200. It was observed to have the following losses: 35 60 130 200+ 200+
ii. Policy B has a deductible of 50 and a policy limit of 300. It was observed to have the following losses: 55 70 150 300+
You are to fit the loss distribution with the maximum likelihood estimation.
Construct the likelihood function.

My question is this:
In (ii) we are given a deductible of 50 and a policy limit of 300. For the likelihood function, it is my understanding that, for 300+, the function is S(u)/S(d) where u is the "maximum covered loss" and not the "policy limit". Why don't we add the deductible to the policy limit to get the maximum covered loss, rather the policy limit is used?
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Old 01-25-2018, 03:29 PM
Academic Actuary Academic Actuary is offline
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I think it has to do with ambiguity of the term policy limit, where in this case it means max covered loss. If it meant max benefit payable you would know the amount of loss if it was between 300 and 350.
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Old 01-25-2018, 04:22 PM
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Note that in some cases, you apply the policy limit (call it L) before applying the deductible (d); giving a maximum covered loss of u = L - d.
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Old 01-25-2018, 06:46 PM
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Quote:
Originally Posted by Academic Actuary View Post
I think it has to do with ambiguity of the term policy limit, where in this case it means max covered loss. If it meant max benefit payable you would know the amount of loss if it was between 300 and 350.
The official textbook defines policy limit to be the maximum possible payment. Although at least one old exam question meant something else by the term, so far as the official text is concerned there is no ambiguity.
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