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Pareto claims under excess of loss

Paper A style · Losses and reinsurance · Straightforward · 8 marks

Individual claim amounts on a household contents portfolio follow a Pareto distribution with parameters $\alpha=4$ and $\lambda=2{,}400$ , so that $F(x)=1-\left(\frac{2400}{2400+x}\right)^{4}$ for $x$ $>0$ . The insurer has an individual excess of loss reinsurance treaty with retention £2,000.

(i)
Calculate the probability that a claim involves the reinsurer, to 4 significant figures.
1 mark
Your answer
(ii)
Calculate the insurer's expected payment per claim, to the nearest penny.
3 marks
Your answer
(iii)
Calculate the reinsurer's expected payment on a claim that involves the reinsurer, to the nearest penny.
2 marks
Your answer
(iv)
Hence calculate the reinsurer's expected payment per claim (including claims that do not involve it), to the nearest penny, and check your answers against the mean claim amount.
2 marks
Your answer

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Random variables and distributions for risk modelling, 20%

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