In a paper that you can dowload here and the two following videos, Dr David Hillson, The Risk Doctor, exposes the concept of « Risk Appetite » and most importantly how to best and most efficiently deal with it.

« One of the most important decisions for any business, project or individual is how much risk to take.
The phrase “risk appetite” is often used to describe the level of acceptable risk, but there is no accepted definition for this term. Even worse, there is confusion between risk appetite and other risk-related terms, especially risk attitude.
In seeking to answer the “How much risk…?” question, this paper considers a range of risk terms, showing how they relate to one another. This reveals that two risk-related factors are particularly influential when individuals or organisations decide how much risk can be taken in a risky and important situation.

These two key factors are risk appetite and risk attitude which have central and complementary roles.
We explain how to use both risk appetite and risk attitude to set appropriate risk thresholds in any given situation. Risk appetite is an internal tendency to take risk in a given situation, and it reflects organisational risk culture and the individual risk propensities of key stakeholders. But unmanaged risk appetite can lead to the wrong outcome. Risk attitude is a chosen response to risk, driven by perception, and it can act as a control point to ensure that the right amount of risk is taken, so that the achievement of objectives is optimised. Putting both risk appetite and risk attitude together into a single framework (the RARA Model) provides a practical approach that enables individuals and organisations to take the right risks safely. »
Overview:
In depth session: