This paper investigates the influence of a stochastic variation of both energy and economic parameters in an optimization loop applied to a refurbished social housing building. Usually, energy and economic optimization procedures rely on the results of an underlying numerical deterministic model which influences both energy gains and economic figures. However, an analyst must always face the random variation of input and parameter data. The unknown data can represent poor initial information or data that can change in a long time; this is the case of fuel cost and economic indexes in particular. This paper deals with both problems for building refurbishment optimization, the former related to the initial state of a building, and the latter to the energy cost variability. Reliability analysis considers a stochastic variation of parameters looking for solutions that incorporate a risk level; in this case, it deals with optimization objectives related to different impacts on economic, environmental and health aspects. The considered building represents a social house, and the energy reduction measures involve the application of internal insulation layers to the walls and the replacement of existing windows with more efficient ones.