Claim limit and ASM 8.19

[MathinTucson]

I need some clarification on the meaning of "claim limit." I thought that it was synonymous with "policy limit" and meant the maximum amount that the insurer would pay on a claim. But in question 8.19 in the ASM manual (from a CAS exam) the deductible is $500 and the claim limit is $25,000. The question requires the expected payment per loss, which I thought would be E[min(X,25,500)] - E[min(X, 500)] since a loss of 25,500 would result in payment of 25,000. But the answer in the manual uses E[min(X,25,000)] - E[min(X, 500)], which implies that the claim limit is the same as the maximum covered loss in this question.
Can anyone clarify?

[its_me]

Claim limit is policy limit
You always apply Policy limit first and then apply deductible to ground-up losses.

Remember , for a ded d and a limit L,
expected payment per loss = E [X ^L] - E[X^d]

Replace with d=0 or L= infinity as the case can be , where E[X ^ infinity] = E[X]
and E[X ^0] = 0 .

For expected payment per NONZERO pmt, divide what you get above with S(d)

Hope this helps

[its_me]

In the example you mentioned, we are talking about LOSSES: there is no SHIFTING yet.
What you have done is applied the Shifting .Please correct me if i am wrong.

[MathinTucson]

Thanks, but what is the source of your information on applying the policy limit first? Prof. Weishaus states in the ASM manual that "the general rule is that the deductible is first" (p. 107). He gives an example of a deductible of $500, claims limit of $10,000, coinsurance of 80%, and a resulting maximum covered loss of $13,000 (=500 + 10,000/0.8).

[its_me]

I am refering to Mahler ( pre-conversion course M for the loss models part)
Mahler says, you apply the Policy limit ,then the deductible and then the coinsurance.

Can someone please confirm this?

[Abraham Weishaus]

Claims limit and policy limit are not the same. I posted an erratum on Sunday dealing with this.

[its_me]

MathinTuscon,here it is, in case u havent seen it

http://www.geocities.com/aweishaus/ErrataC-5d.pdf

I don't think i am understanding it. In both cases, you dont get paid more than L if your loss exceeds L

In Max covered loss, what happens if loss exceeds the claims limit? The insurer pays L and the rest is absorbed by the insured.

In policy limit , what happens if loss exceeds the policy limit? The insurer pays L and the rest is absorbed by the insured.
I am not able to see a difference.

Can I please have an example to differentiate between the two?

[Gandalf]

(My interpretation of Abe's errata) If no deductible and no coinsurance, they are the same. Otherwise, they are different.

Suppose policy 1 has ordinary deductible of 1,000; maximum covered loss of 10,000 and no policy limit. Suppose policy 1 has ordinary deductible of 1,000; no maximum covered loss; and policy limit of 10,000.

Suppose there is a loss of 15,000.

Policy 1 says "maximum covered loss is 10,000, so we treat your loss as 10,000. Deductible is 1,000; here's your check for 9,000."

Policy 2 says "no maximum covered loss, so 15,000. Deductible is 1,000, that leaves 14,000. Policy limit, the most we will pay is 10,000: here's your check for 10,000."

[Abraham Weishaus]

Yes, that's correct.

Perhaps another way to put it is that the claims limit is a number that is stated in the policy, and defines a parameter of the formula for what the insurer will pay. The policy limit is a calculated number, which takes into account deductibles, claims limits, and coinsurance; it is the most the insurer will pay as a result of these coverage modifications.

[its_me]

Does this mean, that when there is a policy limit, we apply policy limit and then the ded and When there is a claims limit, we always apply ded first and then the claims limit?

Edited :Above is wrong ,
For policy limit, we apply ded , coinsur & then max it out at the policy limit before pmt.
For claims limit, we max it out at the max covered loss & then apply the ded , coinsur