Weather-related risk makes the insurance industry inevitably concerned with climate and climate change. Buildings hit by pluvial flooding is a key manifestation of this risk, giving rise to compensations of the induced physical damages and business interruptions. In this work, we establish a nationwide, building-specific risk score for water damage associated with pluvial flooding in Norway. We fit a generalized additive model that relates the number of water damages to a wide range of explanatory variables that can be categorized into building attributes, climatological variables and topographical characteristics. The model assigns a risk score to every location in Norway, based on local topography and climate, which is not only useful for insurance companies, but also for city planning. Combining our model with an ensemble of climate projections allows us to project the (spatially varying) impacts of climate change on the risk of pluvial flooding towards the middle and end of the 21st century.