Risk Function: Definition

Statistics Definitions >

What is a Risk Function?

The risk function is the expected value of a loss function. In other words, it’s the expected value of a loss.

Most losses are not random; They are usually a result of a set of circumstances or decisions that can be quantified. If you have substantial knowledge about a particular process or event, then you can create a risk function for it. As an example, risk has already been widely defined for credit-worthiness; a person with a good credit score income is a better risk than someone with poor credit and few resources.

Defining a Risk Function

The risk function is dependent on the chosen decision rule, which is used in the face of uncertainty. A separate risk function is defined for each consequence scale. Therefore, each asset is linked to a separate risk function.

The basic steps for defining a risk function:

  • Create a matrix for each consequence scale. Place the consequence scale vertically and likelihood scale horizontally.
  • Decide on a risk value for each cell entry. This decision is based on analysis of the specific situation or asset. As an example, it’s fairly easy to decide on risk functions for extremes (e.g. catastrophic/certain or insignificant rare). Values “in between” are usually agreed upon by a panel of experts (e.g. data analysts, management).

Risk Levels

A risk function gives a risk level for every combination of likelihood and a consequence (Lund et al., 2013). Risk levels can be qualitative or quantitative, depending on the choices you made for the likelihood and consequence values.


Lund, M. et al. (2010). Model-Driven Risk Analysis: The CORAS Approach. Retrieved July 29, 2019 from: https://books.google.com/books?id=X4lpi3stRvYC

Comments? Need to post a correction? Please Contact Us.