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This is in response to Arumugam Sutha's question. I think the CAS'
answer is right. (I appreciate John Donaldson's assistance with this
question.)
The payments are being made 25% each at times 1,2,3,4. The average
payment date is time 2.5. The time anything spends as a reserve is from
time 1.0 (set up reserve at end of year one) to the average payment
date, or 1.5 years. Taking 1.5 (reserve/loss ratio) times 0.8
(loss/premium ratio), equals 1.2 reserve/premium ratio. Everything else
follows from this.
Another way of looking at this: once three years are written (draw up a
little chart by year and payment, and ignore the payment at time 1 since
it would be paid not reserved for), the system achieves a steady state
and the most recent year will need a reserve of .75, the prior year 0.5,
and the next prior year 0.25. Adding gets 1.5, times 0.8, is 1.2.
If I pass this exam, you may glimpse me driving around in a red '97
Ferrari. Furrari? What ever.
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