Special distribution shortcuts if there's a deductible: the post-deductible distribution for a Pareto claim is which of the following?

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Multiple Choice

Special distribution shortcuts if there's a deductible: the post-deductible distribution for a Pareto claim is which of the following?

When a deductible is applied to a Pareto claim, the part of the claim that remains payable after the deductible still follows a Pareto form, but with a shifted threshold. If the original claim X is Pareto(Alpha, Theta) and you have a deductible d, the post-deductible amount that is paid (assuming the claim exceeds the deductible) behaves like a Pareto with the same shape Alpha but with a new threshold Theta' = Theta + deductible. In other words, the tail of the post-deductible payout matches the Pareto(Alpha, Theta + deductible) form. This gives a simple shortcut: the distribution after applying the deductible retains the Pareto shape and simply shifts the threshold by the deductible amount.

When a deductible is applied to a Pareto claim, the part of the claim that remains payable after the deductible still follows a Pareto form, but with a shifted threshold. If the original claim X is Pareto(Alpha, Theta) and you have a deductible d, the post-deductible amount that is paid (assuming the claim exceeds the deductible) behaves like a Pareto with the same shape Alpha but with a new threshold Theta' = Theta + deductible. In other words, the tail of the post-deductible payout matches the Pareto(Alpha, Theta + deductible) form. This gives a simple shortcut: the distribution after applying the deductible retains the Pareto shape and simply shifts the threshold by the deductible amount.

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