Investment decisions in adaptation are usually made under significant uncertainty due to climate change and socio-economic trends. In this study, we propose three ways to incorporate climate and socio-economic uncertainty into the assessment of an adaptation infrastructure designed to cope with flood-risk in the city of Bilbao. First, we use stochastic modelling to estimate the present value of expected damage over a time period, considering that extreme events may increase in the future. Second, we develop an additional calculation that incorporates two risk measures used in financial economics: Value-at-Risk and Expected Shortfall, the latter being a less common but better risk indicator. Third, we illustrate a case of Real Options Analysis (ROA) in which a binomial tree is used to study whether the best decision at present is to invest now or to delay the investment decision.