About optimal control of allotment of impartible resource

A dynamic economic system with discrete time is studied. The state of the system is characterized by integer nonnegative points of $\mathbb R^2$. There are two different productions and at each production the state of the system is changing by a stochastic vector with integer coordinates.The control is the choice at each moment of the first or second production. The aim of control is to maximize the probability of survival, i.e. the probability that the states of the system stay in the first quadrant. Existence of an optimal control is proved. Estimates for the probability of survival for news cases are obtain. Bibl. 9.