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# A.1 Market Equilibrium Resolution

Intuitively, two situations shall be distinguished for modeling for each reinsurer whether its solvency constraint is saturated or not. First, in the saturated case, the choice of external capital _Er_ is an implicit function of the choice of supply _Or_ through the solvency constraint.<sup>16</sup> The equilibrium constraint is then equivalent for the concerned reinsurers to the maximization of their expected prot as a function of reinsurance supply only.

> 16In practice, due to the form of the capital costs, there may be two solutions _Er_ to this constraint that lead to the same expected prots. In this case, we take the lower level of capital _Er_ as it gives the highest yield.

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