Before revision: We obtain structural results for non-Markovian optimal stopping problems in discrete time  when the decision maker is risk averse and has partial information about the stochastic sequences generating the costs . Time consistency is ensured in the problem by the aggregation of a sequence of conditional risk mappings, and the framework allows for model ambiguity. A reflected backward stochastic difference equation is used to characterise the value function and optimal stopping times .
After revision: We obtain structural results for non-Markovian optimal stopping problems in discrete time when the decision maker is risk averse and has partial information about the stochastic sequences generating the costs , and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equation is used to characterise the value function and optimal stopping times .