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.

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
• expectile: Expectile

All risk measures, except ERM, are non-decreasing in risk level alpha. The ERM is non-increasing in level beta.

The package currently only supports random variables with descrete probability distributions, but support for continuous probabilty distributions is planned for the future.

Examples

Using arrays

using RiskMeasures

x = [1, 5, 6, 7, 20]
p = [0.1, 0.1, 0.2, 0.5, 0.1]

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

Using random variables

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
expectile(x̃, 0.1)   # entropic risk measure

Using transformed random variables

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

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

Future development plans:

• Analytical computation for special distributions, like Normal and others
• Add an optional intergration with Mosek's exponential cones to support computation of EVaR.
• Coquet capacity risk measures
• General risk measure construction from utility functions, such as CE, OCE, utility shortfall risk measures.
• Phi-divergence risk mesures for any phi-divergence function

See Also

• MarketRisk.jl