Consider a risk-averse decision maker in the setting of a single-leg dynamic revenue management problem. Instead on focusing on maximizing the expected revenue, the decision maker has the main objective of minimizing the risk of failing to achieve a given target revenue. Interpreting the revenue management problem in the framework of finite Markov decision processes, we obtain a dynamic programming solution which generates a policy minimizing risk of not attaining a specified target revenue. We compare this solution with recently proposed risk-sensitive policies in a numerical study.