Stationary uncertainty frontiers in macroeconometric models and existence and uniqueness of solutions to matrix Riccati equations (Q1110438)

We characterize the stationary uncertainty frontiers in dynamic macroeconometric models. This frontier, the definition of which is due to \textit{M. Deleau} and \textit{P. Malgrange} [Eur. Econ. Rev. 12, 17-51 (1979)], is the set of the least positive semi-definite covariance matrices of the objective variables stabilized by stationary policies. We prove that this frontier coincides with the set of the covariance matrices stabilized by optimal stationary non-singular policies. We prove also that solving the matrix Riccati equations with stable feedback controls is equivalent to minimizing a linear form in a closed convex set of covariance matrices of the objective variables. As corollaries of this proposition, we have results on the existence and uniqueness of solutions of matrix Riccati equations.