Coupling different energy infrastructures, i.e. the concept of energy hub (EH), is an efficient approach to the optimal operation of both electrical and natural gas systems. This paper optimizes the risk-constrained scheduling of a wind-integrated smart multi-carrier energy hub (SMEH) and evaluates its operation in combination with compressed air energy storage (CAES) system, an electrical demand response (EDR) program, and a thermal demand response (TDR) program. The proposed SMEH consists of combined heat and power (CHP) units, a CAES system, a thermal storage system, boiler units, and an electrical heat pump (EHP) system. The penetration of wind power generation and application of the CAES system make a dependable condition to the optimal scheduling of the SMEH. The wind turbine generation and electrical and thermal demands are modeled as a scenario-based stochastic problem using the Monte Carlo simulation method. A proper scenario-reduction algorithm is also used to reduce the computational burden. Moreover, the conditional value-at-risk (CVaR) algorithm is merged with the proposed model to propitiate the risk of the high costs relevant to worst scenarios as a proper risk evaluation method. Finally, the proposed system is applied to a studied case to demonstrate the applicability and appropriateness of the proposed method. •The CVaR method is implemented to model the potential risk of SMEH scheduling cost.•EDR and TDR programs are applied to reduce the SMEH operation cost.•CAES is considered as a solution to reduce the volatility problem of wind generation.•CAES provides more freedom in decision making for optimal scheduling of the SMEH.•A stochastic model is used to model the uncertain wind generation and demands.