  A discrete time probabilistic model, for optimal equity allocation and
portfolio selection, is formulated so as to apply to (at least) reinsurance. In
the context of a company with several portfolios (or subsidiaries),
representing both liabilities and assets, it is proved that the model has
solutions respecting constraints on ROE's, ruin probabilities and market shares
currently in practical use. Solutions define global and optimal risk management
strategies of the company. Mathematical existence results and tools, such as
the inversion of the linear part of the Euler-Lagrange equations, developed in
a preceding paper in the context of a simplified model are essential for the
mathematical and numerical construction of solutions of the model.
