Pop Quiz #1
Hi Graham,
why wasn't the claim consided at all in non-financial risk adjustment calculation? Thank you!
Scenario 1:
The insurer is indifferent to these investment choices:
purchase $100,000 in no-risk government bonds with 3% coupons payable annually for 5 years
receive $20,000 to accept an insurance risk with a 90% probability of no claim and a 10% chance of $150,000 claim within 5 years
non-financial risk adjustment = $5,000
(this is the difference between the total coupon payments of $15,000 from the bond and the premium payment of $20,000)
Comments
I just made this example up to try to better understand the concept because the source reading didn't have any examples. But now that I'm looking at it again, I don't think my example makes sense. I made it more complicated than it needed to be. Here's a simpler example to illustrate the risk adjustment concept:
choice 1: the insurer takes on fixed liability with a present value of $15,000
choice 2: the insurer takes on an uncertain liability whose present value has a uniform distribution from $10,000 to $20,000. (The expected present value is $15,000, the same as for choice 1.)
Suppose you offer the insurer payment P1 to accept the fixed liability in choice 1 but a higher payment P2 to accept the uncertain liability in choice 2. Suppose also the insurer says they are indifferent to these choices.
Question: What is the risk adjustment?
Answer: The risk adjustment is the difference P2 - P1. This is the compensation required to make the riskier choice 2 as attractive as the less risky choice 1. (If the insurer was offered less than P2 for choice 2, they would prefer choice 1, but if they were offered more than P2 for choice 2 they would prefer choice 2. In each case, the insurer would no longer be indifferent.)
I think I need to delete that Pop Quiz and insert a link to this new example. Please let me know if you have any comments. Thanks.