RiskMeasures

Warning: This is package is under development and the computed values should be treated with caution.

Julia library for computing risk measures for random variables. The random variable represents profits or rewards that are to be maximized. Also the computed risk value is preferable when it is greater.

All risk measures get more conservative with an increasing risk level alpha.

The following risk measures are currently supported

• VaR: Value at risk
• CVaR: Conditional value at risk
• ERM: Entropic risk measure
• EVaR: Entropic value at risk

The focus is currently on random variables with categorical (discrete) probability distributions, but continuous probabilty distributions may be supported in the future too.

In general, the smaller value of the risk parameter indicates that the risk measure is less risk-averse or that it is closer to the expectation operator.

using RiskMeasures
using Distributions

x̃ = DiscreteNonParametric([1, 5, 6, 7, 20], [0.1, 0.1, 0.2, 0.5, 0.1])

VaR(x̃, 0.1)   # value at risk
CVaR(x̃, 0.1)  # conditional value at risk
EVaR(x̃, 0.1)  # entropic value at risk
ERM(x̃, 0.1)   # entropic risk measure

We can also compute risk measures of transformed random variables

VaR(5*x̃ + 10, 0.1)   # value at risk
CVaR(x̃ - 10, 0.1)  # conditional value at risk

Extended methods VaR_e, CVaR_e, and EVaR_e also return additional statistics and values, such as the distribution that attains the risk value and the optimal β in EVaR.

Please see the unit tests for examples of how this package can be used to compute the risk.

• Analytical computation for special distributions, like Normal and others
• Add an optional intergration with Mosek's exponential cones to support computation of EVaR.

• MarketRisk.jl