3 Optimizing conditional value at risk is more generally discussed in It implements conditional value at risk as an optimization formulation used as a convex combination with the expected value. I became interested in risk measures from developing DecisionProgramming.jl, a Julia library for decision-making problems under uncertainty. julia> conditional_value_at_risk(x, f, α) Then, executing the function in Julia REPL gives us a result. Note that the states $x$ do not have to be unique for the formulation to work. Next, we assert that the inputs are valid. Scale(v, low, high) = v * (high - low) + low Let us create a random discrete probability distribution. A coherent risk measure is a function $ρ:V→ℝ$ that satisfies the following properties: Coherent Risk MeasuresĬonsider a set $V$ of real-valued random variables. This article aims to make it easy and fast to implement and understand Conditional Value at Risk, whereas the original article is quite laborious to understand. We recommend reading the original paper 1, which covers the formula’s full derivation, proofs, and discussion. As a concrete example of a coherent risk measure, we introduce conditional value at risk, also known as the Expected Shortfall. They have properties that make them applicable for fields such as finance and efficient for mathematical optimization. For example, a lawsuit might destroy a small company, but large companies often have legal teams just for handling cases, making them operational costs.įor quantifying risk, we explore a class of risk measures called coherent risk measures. The difference between what is considered small and large risks depends on the size of the entity. In real-life, risks outside the model exists, and their outcomes may be significant. However, keep in mind that models can only quantify risks it accounts for, not risks outside the model. Thus, the purpose of quantifying risk is to minimize the chances of catastrophic events. If the entity has to slow or halt its activities, it can no longer produce a positive upside, such as monetary profits. It can be difficult or impossible to recover from a catastrophic event hence, they may pose an existential threat to the entity. On the other hand, large risks, aka worst-case risks, include catastrophic events such as bankruptcy, injury, or death. The designs may increase sales and result in profits or fail, and result in losses. For example, a business can spend time and money to test new product designs. We can think of small risks as operational costs resulting in lost resources, such as time, money, and effort in amounts that can be justified by the potential profits and do not threaten existence. We refer to negative outcomes as downside or cost and positive outcomes as upside or profit.įirst, we need to distinguish the difference between small and large risks. We will use analogies form these fields to explain the concepts related to risk and uncertainty. We find these processes from fields such as finance, economics, and biology in real life. This article explores how to measure the risk of processes that involve uncertainty.
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