Risk is defined as the downside of a gamble which is described in terms of probability. They further note that risk is multidimensional, i.e. there are many possible damage measures. Finally, they extend the definition of risk to a probabilistic family of multidimensional curves, which include the first level definition of risk. For the mathematically inclined, very interesting concepts are to be found here. Risk is individual to a person or organization because what is perceived by one as a major risk may be perceived by another as a minor risk.
Perception is very much a factor.
To some, risk is defined as the chance of loss. But in reality it is more. Risk also concerns how much could be lost. Probabilistic risk analysis can define risk as the expected loss, or even as a family of probability curves. This has to do not just with the chance of loss, but more specifically with the extent of loss.