Equilibria in a proportional reinsurance market

The classical theory is adapted to the situation where the risk exchange of n insurance companies is an exchange of payments that belong to a certain linear class of random variables, for example the payments corresponding to certain layers of the aggregate claims. Similarly, a price equilibrium is considered, where the companies can purchase payments of a linear class. An example is the case where each company buys proportional coverage for its own claims and sells proportional coverage for the claims of the other companies.