A building energy system includes equipment and an asset allocator configured to determine an optimal allocation of energy loads across the equipment over a prediction horizon. The asset allocator generates several potential scenarios and generates an individual cost function for each potential scenario. Each potential scenario includes a predicted load required by the building and predicted prices for input resources. Each individual cost function includes a cost of purchasing the input resources from utility suppliers. The asset allocator generates a resource balance constraint and solves an optimization problem to determine the optimal allocation of the energy loads across the equipment. Solving the optimization problem includes optimizing an overall cost function that includes a weighted sum of individual cost functions for each potential scenario subject to the resource balance constraint for each potential scenario. The asset allocator controls the equipment to achieve the optimal allocation of energy loads.