Exercise $15$

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:

a$)$ Quota Share $40\%$ unlimited

b$)$ Surplus $Z=2$ million; $L=3$ lines of cover

c$)4$ million XL over $5$ million

Due to own capital the cedant's own insurance capacity amounts to $10$ million. Calculate the

cedant's maximum face value on policy underwritten in regard with reinsurance programme. The answer is $33,33.$ Please provide detailed explanation, thank you