Average Accident Date of Future Accident Year?
I'm having trouble understanding this part of the discount factor equation. The other parts of the calculation seem intuitive to me - claim payments, as well as the average accident date of UPR are both in the future (relative to the valuation date), so the impact of discounting is favourable. But what is the average accident date of the future accident year, and why does it produce an unfavourable discounting impact (i.e. shortening the discounting period by 0.5 years)?
Comments
When you mean favourable impact, you mean increasing the PV factor by (1+i)^(0.5-1/3)?
This is because the average accident date is not the midpoint and is a little closer for premium liabilities compared to unpaid claims. The source shows a proof on page 14 which involves a lot of calculus. I wouldn't bother and just take it as a given