Résumé en anglais

One considers a many-commodity world where technology depends on an exogenous environment whose successive states form a stationary Markov process. A program is optimal if it overtakes any other program or has the maximum expected utility. It is shown there exists a best stationary program. One proves then there exists an optimal program, which converges asymptotically to the best stationary program, and is generated by a policy such that, at every date, a nonrandom production decision is chosen which depends only on the state of the world and of the economy at that time.