Abstract. Typical model used in many fields of applied mathematics regarding selection of optimal decisions in stochastic systems is considered. The multidimensional death process controlled on an interval of random length, which is analyzed in the paper, can be used to describe phenomena that appear in economical, biological, medical, engineering, and other applications. Several approached are proposed to determine the of optimality criteria, the properties of corresponding risk function are investigated, and a computing algorithm is developed for construction of optimal stationary strategies.

Keywords: optimal stationary strategies, controlled processes, Markov decision processes, risk function, birth-death processes, iterative algorithms.