Finance and the Earth system – Exploring the links between financial actors and non-linear changes in the climate system

•Financial capital plays a key role in economic activities around the world, as well as in efforts to avoid climate change.•We develop a methodology that link financial actors to industries modifying tipping elements in Earth’s climate system.•We identify “Financial Giants” who through their ownership have considerable influence over climate stability.•We assess the incentives of “Financial Giants” to collaborate and use their influence to help stabilize tipping elements.