An improved algorithm to solve a discrete matrix Riccati equation (Q749484)

For the linear econometric dynamic model \(X_ t=AX_{t-1}+BU_ t\), \(t\in N\), \(X_ t\in R^ n\), \(U_ t\in R^ q\), the objective function \(V=\sum^{T}_{1}(X_ t'QX_ t+U_ t'RU_ t)\), Q, R symmetric positive, \(Q\geq 0\), \(R\geq 0\) is considered in a finite-horizon stabilization problem. The paper presents an efficient algorithm which takes into account some features of optimal control problems in applied economics such as: rank Q is generally small, q is far smaller than n etc. The algorithm is based on a factorisation of the matrix Riccati equation and was suggested by various approaches in engineering science. Its efficiency is proved on an example using a French macroeconometric model.