You are the actuary for a reinsurance company. An insurance company, A, wants to buy a layer of excess-of-loss reinsurance (£10M × £5M) for its property portfolio from your company. The underwriter has asked you to produce a price for this product by loading the expected losses to this layer by 40%.

You decide to price this excess-of-loss policy based on a combination of experience rating and exposure rating and combine them with a credibility approach

a. Describe what data you would require company A to provide to perform experience rating and exposure rating. Make a separate list for the two rating methods, although some items may be the same.

As a result of the experience rating exercise, you estimate that the expected losses to the layer will be £100,000 ± £30,000, where £30,000 is the standard error, which you obtained by error propagation methods based on the parameters of the frequency and severity distribution.

As to your exposure rating exercise, you reckon that the portfolio of company A is made of approximately similar types of property whose loss curve can be approximated as a Swiss Re curve with the same value as parameter c.

You estimate that the value of c is distributed as a normal distribution centred around c = 5.0 with a standard deviation σ

(c) = 0.5 (all properties have the same value of

c, but the exact value of c is not known). As a result of this, your exposure rating calculations yield the following values for the exposure-based losses: £150,000 with a standard deviation of £70,000 (the standard deviation of £70,000 is related to the uncertainty on the parameter c).

b. Write a credibility formula that combines the experience rating and the exposure rating result, and a formula you would use to calculate the credibility factor Z. Explain what the terms in Z are and why it makes sense to apply the formula to this case.

c. Use the formula in

(b) to produce a credibility estimate for the premium.