Demand response and real-time pricing of electricity are key factors in a smart grid as they can increase economic efficiency and technical performances of power grids. This paper focuses on incorporating price-responsive customers in day-ahead scheduling of smart distribution networks under a dynamic pricing environment. A novel method is proposed and formulated as a tractable mixed integer linear programming optimization problem whose objective is to find hourly sale prices offered to customers, transactions (purchase/sale) with the wholesale market, commitment of distribution generation units, dispatch of battery energy storage systems and planning of interruptible loads in a way that the profit of the distribution network operator is maximized while customers' benefit is guaranteed. To hedge distribution network operator against financial risk arising from uncertainty of wholesale market prices, a risk management model based on a bi-level information-gap decision theory is proposed. The proposed bi-level problem is solved by recasting it into its equivalent single-level robust optimization problem using Karush-Kuhn-Tucker optimality conditions. Performance of the proposed model is verified by applying it to a modified version of the IEEE 33-bus distribution test network. Numerical results demonstrate the effectiveness and efficiency of the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.