10-10 rule Capping the Loss at Retention plus Excess

For the 10-10 rule, I take it the excess layer kicks in at (retention + excess) and that's why we cap the gross loss at that amount?
Thanks!

Comments

  • I think I would phrase it as: the excess layer kicks in at the retention point.

    If:

    • retention = 8m
    • excess coverage = 10m

    then the excess layer kicks in after losses reach 8m. The reinsurer would then cover any amounts in excess of 8m up to 18m. If losses exceed 18m, the reinsurer would not provide any more coverage so that's where the capping would come in.

    If:

    • total loss = 15m

    then the reinsurer would cover 7m and they would calculate PV(7m) in the 10-10 rule calculation.

    But if:

    • total loss = 20m

    then the reinsurer would only cover 10m (not 12m). This is where you would cap the gross loss at (retention + excess) = 18m and the reinsurer would calculate PV(18m - 8m) = PV(10m) in the 10-10 rule calculation, not PV(20m-8m).

    Hope that helps!

  • Awesome, thanks for the detailed explanation to help me understand!

  • Related to the 10-10 rule, why do we calculate the NPV(loss) = PV(gross loss - retention)? Why wouldn't it be NPV(loss) = PV(gross loss - retention) - PV(reinsurance premium)?

  • Well, you can do it either way. The way I did it in the practice problem is to check the following inequality:

    • PV(gross loss - retention) > 110% x (reinsurance premium)

    But you can rewrite this inequality as:

    • PV(gross loss - retention) - 100% x (reinsurance premium) > 10% x (reinsurance premium)

    So the left side equals what you wrote in your post. It just depends on how you define NPV, whether it refers just to loss or whether it refers to total profit.

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