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April 2019 IFoA QP Qn # 8

vidhya36

vidhya36

Very Active Member
How did the author arrived at the percent cover exhausted to 8% on 12.5M to calculate the Reinstatement Premium in this question?

The XoL covers the $2.5 to $17.5 layer. $15M is the loss from the EQ event, out of which, 2.5 will be borne by the insurer itself. So, the Reinsurer covers 12.5 M. What I have calculated so far is (12.5/15 = five sixth of the layer) 5/6 th of the layer is exhausted. So, shouldn't the reinstatement premium be 5/6 * 15? What am I missing here?

Any help is much appreciated.
TIA
 
You need to apply the 5/6 that you have correctly calculated to the full reinstatement premium for the layer, not to the width of the layer.

We are told that the rate on line is 8% and the reinstatement premium is 100% of original premium.

Full reinstatement premium is therefore 100% * 8% * $15m=$1.2m.

Since we have only burnt through 5/6 of the layer, reinstatement premium due following the XoL recovery on earthquake loss
= 5/6 * $1.2m = $1m.
 
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