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[actuaryinmaking]

Que.1 Individual claim amounts from a non-life insurance portfolio have an Exponential distribution with parameter 0.00006. The insurer arranges an excess of loss reinsurance treaty with a retention limit of $50000 on any claim for this portfolio, so that the insurer pays the whole of a claim if it is $50000 or less but pays only $50000 for any claim which exceeds this amount. If an individual has two policies find the following:

(i) The probability that the reinsurance will involve in respect of claims under both policies.
(ii) The total claims under both policies is less then $50000.


Que. 2 The individual claim size from an insurer’s portfolio has a log-normal distribution with parameters (10, 0.81). The insurer is considering taking an excess of loss reinsurance treaty with retention level of $40000. Find the mean of the net claims payable by the insurer.

(i) without reinsurance treaty
(ii) with reinsurance treaty

Que. 3 Claims from a portfolio are believed to have a Pareto Distribution with parameters (8, 2000). An excess of loss reinsurance treaty is arranged with a retention limit of $900. Inflation is a constant 10% per annum. Find the following :
(i) The mean amount payable by the insurer without allowing for inflation.
(ii) The mean amount payable by the insurer allowing for inflation


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