Financial risk management is the practice of protecting economic value in a firm by managing exposure to financial risk - principally credit risk and market risk, with more specific variants as listed aside - as well as some aspects of operational risk. As for risk management more generally, financial risk management requires identifying the sources of risk, measuring these, and crafting plans to mitigate them. See Finance § Risk management for an overview.
Financial risk management as a "science" can be said to have been born with modern portfolio theory, particularly as initiated by Professor Harry Markowitz in 1952 with his article, "Portfolio Selection"; see Mathematical finance § Risk and portfolio management: the P world.