Exercise 16

The insurer operates under the obligatory reinsurance programme. The programme combines in a hierarchical order three types of cover: Quota Share at the bottom, then Surplus and the Excess of Loss on the top. The Surplus secures retention left after Quota Share and the Excess of Loss secures retention left after the Surplus. Below are details on each type of cover:

1. Quota Share 40% up to 30 million
2. Surplus Z=2 million; L=3 lines of cover
3. 4 million XL over 5 million

Due to own capital the cedants own insurance capacity amounts to 20 million. Calculate the cedants maximum face value on policy underwritten in regard with reinsurance programme.

{Hint: First find the cedants retention in the point when all reinsurance covers are exhausted, i.e. start with a risk of 30 million. The cedant will retain 18 million after QS, 12 million after SUR and 8 million after XL. Thus a policy with a face value of 42 million should exhaust the remaining cedants capacity resulting from own capital endowment}