Financial risk management avoids losses and maximizes profits, and hence is vital to most businesses. As the task relies heavily on information-driven decision making, machine learning is a promising source for new methods and technologies. In recent years, we have seen increasing adoption of machine learning methods for various risk management tasks. Machine-learning researchers, however, often struggle to navigate the vast and complex domain knowledge and the fast-evolving literature. This paper fills this gap, by providing a systematic survey of the rapidly growing literature of machine learning research for financial risk management. The contributions of the paper are four-folds: First, we present a taxonomy of financial-risk-management tasks and connect them with relevant machine learning methods. Secondly, we highlight significant publications in the past decade. Thirdly, we identify major challenges being faced by researchers in this area. And finally, we point out emerging trends and promising research directions.