The possibility that a negative event (such as a loss) will happen.

Risk is a major components of how quants see the financial world:

  • on the one hand you have anticipation of the future prices (or flows, that is almost equivalent given the information set, i.e. the filtration, that you have access to),
  • on the other hand you need to fear the uncertainty about the future. The "risk" is this second kind of information you have to process.

Very often writing together the directional knowledge and the risks leads to an optimization that, as a quant, you can solve in closed form formula or using numerics.

It is how one can write Hamilton-Jacobi-Bellman equations (for instance in the realm of derivative pricing or optimal trading) or mean-variance optimizations (like in asset management and portfolio construction).

Another very important view on the risk concerns the way market participants form a network of agents exchanging risks. For instance structurers of derivative products package different risks (i.e. payoffs on future value of some factors) and sell them to asset managers. It transfers some risks from their balance sheet to the one of asset managers, who at their turn package them with other exposures to build investment vehicles that are sold, either to other asset managers, either to asset owners. See Financial Markets in Practice: From Post-Crisis Intermediation to FinTechs, by Lehalle and Raboun (2022) for details.