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DETAIL: You work for an insurer, NewBright Insure, and have been tasked with developing innovative insurance that will indemnify other insurers if one or more of their reinsurers file for bankruptcy.

**BACKGROUND NOTE**

All insurance companies share their risks with reinsurers; typically, there may be ten or more entities on each reinsurance product procured- there may be , for example, several reinsurers in different countries who will share the risk of claims on large industrial properties.

If a reinsurer cannot pay their share of a loss, the reinsured has to carry an increased share of an original loss.

This new insurance , called CAPITAL LOCK, will pay up to a maximum of Euro 100,000 for unrecoverable sums in respect of any reinsurer. The reinsurer must have lodged formal liquidation or bankruptcy papers for this policy to function.

You have to provide a report that explores the risk and underwriting implications of this plan.

Information and data available to you includes:

(i) research , involving a study of reinsurer insolvency, suggests a 0.02 ( 2 %) risk of failure of any reinsurer,

(ii) the sample suggests claims can only cost the following amounts

( i.e. these are the only possible claim sizes)

25,000 25,000 25,000 38,000 38,000 69,000 80,000 100,000.

Your report should:

(a) critically discuss the insurability aspects of this innovation and describe how you would personally manage the risks here,

(b) (i) statistically summarise and comment on the claims information provided and determine a basic premium,

(ii) looking at the indicated frequency rate, how confident are you that this is reliable?

(c) it is anticipated that 800 insurances will be sold in a year:

(i) find the total risk premium

(ii) find the standard deviation

(d) assuming only losses of a standard amount of 50,000 can occur, what is the probability of incurring total losses beyond 1,000,000; hence what is the likelihood of having three such years in five?

(e) find the cost of a stop loss reinsuring beyond 20 losses

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