General Insurance Question!

Can some one please explain the following questions to me as I am having some trouble in answering them! Thank you for any help in advance.

1. A fellow student has stated that the theoretical way that quota-share and surplus reinsurance are priced must be incorrect as both simply pay the reinsurance company the relevant percentage of premium. However, as surplus reinsurance is more risky the reinsurer should DEMAND relatively LARGER PREMIUMS for surplus reinsurance. Discuss this statement.

2. A surplus reinsurance treaty is offered by reinsurance company A with 9 lines and a maximum retention of £100,000. In addition a second treaty is also set up with another company, reinsurance company B, that gives an additional 10 lines. This second treaty is only used when the first treaty has used all the lines with maximum retention. For the following two risks
RISK 1: EML - £400,000 CLAIM - £240,000
RISK 2: EML - £1,500,000 CLAIM - £1,000,000

Calculate the CLAIMS PAID by the companies if the direct insurer uses;
a.) Maximum retention
b.) Minimum retention

Also what are the advantages of having the second treaty in place?

 

proportional ri

1.) my understanding is that the 'pricing' of these proportional treaties is just reflected in the commission rates agreed, particularly the override commission, and profit commissions, so its reasonable to assume these would typically be more favourable for a reinsurer for a surplus treaty compared to a quota share. (However, I don't think this is discussed in ST7 notes, so, personally I wouldn't worry about it for the purposes of the ST7 exam). I suspect the underwriting controls may also be typically stricter for a surplus compared to a QS.

2.a) Risk 1: max retention: 100k, ceded 300k (3 lines to treaty A) => 25%/75% split of exposure and claims => claim of 240k would be split 60k(insurer)/180k reinsurer A

Risk 2: max retention: 100k, ceded 1,400k (14 lines: 9 to treaty A, 5 to treaty B) => split: 6.67% (insurer)/60% (reinsurer A)/33.33% (reinsurer B) => claim of £1m split in these proportions: 66.67k (insurer)/600k(reinsurer A)/333.33k (reinsurer B)

2.b) Risk 1: minimum retention will mean ceding 9 lines, so insurer keeping 10% => keep £24k of claims, insurer A takes the remaining £216k
(remember treaty B is not available if you don't keep the max retention)

Risk 2: see answer (a) for risk 2

Advantages of having second treaty:
so you can write bigger risks (without the problems associated with fac)