A discrete time finite horizon stochastic control problem is considered whose dynamic equations and loss function are linear in the state vector with random coefficients, but which may vary in a nonlinear, random manner with the control variables. The controls are constrained to lie in a given set. Surprisingly, the optimal control or policy for this set is independent of the value of the state--a fact that follows from a simple dynamic programming argument concerning the form of the optimal return function. Under suitable restrictions on the functions, the dynamic programming approach leads to efficient computational methods for obtaining the controls via a sequence of mathematical programming problems in fewer variables than the number of controls in the entire process. 11 pp. Ref.
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