This paper considers the "inventory outsourcing problem" when the supplier is a leader having full information of the outsourcing firm's demand distributions and parameters. This leads to a Stackleberg game which is solved under a number of cases. Both demand dependent and independent models are considered, the latter resulting from (statistical) risk aggregation of firms’ demands operating in correlated markets. A number of examples are also solved in order to highlight essential risk related and costs issues underlying inventory outsourcing. For practical purposes, a scenario based linear programming problem is formulated to resolve the supplier’s problem in any scenario set.