Parameter Risk and use of pricing assumptions

jc2018

Hi,

Under parameter risk section (page 19) it says that "accounting for this increased variability in your simulation will increase the likelihood that ... risk transfer is present". Doesn't this mean the action we take (accounting for risk implicitly or explicitly) will decrease the variability that was creased by the parameter risk? If so, why does this increase the likelihood that we determine the risk transfer to be present?
I see that to "account for parameter risk" the implicit method says to use "slightly higher expected loss selection" or to "increase the expected volatility of losses" so I see that this would probably increase the projected loss and the likelihood of risk transfer.

But then why does it say to use less conservative selections in the pricing assumptions section(Pg.21 2nd paragraph)?
Aren't we just off-setting what we did in parameter risk selection?
It also says "selecting the higher expected losses and increasing the expected variability would lead to over-detecting risk transfer".
Going back to my first sentence, it seems to say that under Parameter risk, it says that we need to account for the increased variability but that it will lead to over-detecting risk transfer. But under Premium assumption risk, it seems to say that if we DO NOT account for the increased variability due to higher expected losses from conservative selections, THEN it will lead to over-detecting risk transfer.
It seems to say two opposite things so I'm a bit confused.

chrisboersma

This doesn't answer your question?:

This is a reasonable result when you consider that the reinsurer is clearly accepting this same parameter risk when entering into the contract.

Ignoring parameter risk ignores a risk the reinsurer has themselves

Use of Pricing Assumptions for Detecting Reinsurance

Notably, when pricing a reinsurance contract, it might be considered prudent to make conservative selections...These selections would not be considered conservative in a risk transfer analysis

If we use pricing assumptions to detect risk transfer we need to be cognizant that conservative pricing selections were likely used by reinsuerer (beyond all the actual risks we would normally expect: claim risk, timing risk, parameter risk, etc.).

When we use pricing for detection we are going to use some function of premiums to determine some loss information (premium -- > frequency x severity). If premiums are exaggerated (due to excessive margins) our claims estimates will be exaggerated by that same amount: that is bad to reinsurance detection. We need accurate loss distribution to detect reinsurance transfer.

graham

Hello jc2018, let me add a few comments to the above response. I read your question and the text, and I didn't see that there was any contradiction between p19 and p21. Here's how I made sense of it in my own head. You can let me know if this makes sense to you or if you'd like to discuss further:

Let's take a step back a look at the risk transfer test from a general perspective. There are 2 types of errors you could make when doing a risk transfer test:

• (A) conclude there is risk transfer when there isn't
• (B) conclude there isn't risk transfer when there is

The insurer and reinsurer have different ideas on what is "good".

• The reinsurer prefers error (A). (They get credit for assuming risk when they really haven't.)
• The insurer prefers error (B) (The may get more favorable treatment in terms of lower premiums if the risk transfer test is negative when in reality they are getting the benefit of transferring risk.)

So, the idea of "conservative" is also different for the insurer versus the reinsurer. The reinsurer would choose a higher expected loss to be conservative in pricing, but the insurer would choose a lower expected loss to be conservative in testing risk transfer.

Now, your question was whether that contradicts the statement on p19 that accounting for parameter risk will over-detect risk transfer. But p19 & p21 are talking about different things:

• p19 says that taking into account parameter risk will over-detect risk transfer (which, from the point of view of the insurer, would be a less conservative way of doing the risk transfer test.)
• p21 is simply explaining the difference between the insurer and reinsurer in the use of the term "conservative".

So, in general, the insurer should be conservative when testing risk transfer (i.e. tend to under-detect and commit error (B)) but if they take into account parameter risk, this may work against their conservatism and cause over-detection. It isn't a contradiction. It's just explaining how different choices affect the outcome of the risk transfer test.

Again, let me know if that doesn't answer your question or if you'd like to discuss further.

jc2018

Thank you I think that clears up the confusion!