  We use one-step conditional risk mappings to formulate a risk averse version
of a total cost problem on a controlled Markov process in discrete time
infinite horizon. The nonnegative one step costs are assumed to be lower
semi-continuous but not necessarily bounded. We derive the conditions for the
existence of the optimal strategies and solve the problem explicitly by giving
the robust dynamic programming equations under very mild conditions. We further
give an $\epsilon$-optimal approximation to the solution and illustrate our
algorithm in two examples of optimal investment and LQ regulator problems.
