CVaR for Gain (cvar_risk_g)
Contents
CVaR for Gain. Conditional Value-at-Risk for -(Linear Loss ) scenarios (also called Expected Shortfall and Tail VaR), i.e., the average of largest (1-α)% of -(Losses).
Syntax
cvar_risk_g(α, matrix) |
short call |
cvar_risk_g_name(α, matrix) |
call with optional name |
Parameters
matrix is a Matrix of Scenarios:
where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.
is a confidence level.
Mathematical Definition
CVaR for Gain function is calculated as follows:
,
where
is CVaR function,
is Loss function (See section Loss and Gain Functions),
is an argument of function.
Example
See also
CVaR,
CVaR Normal Independent, CVaR Normal Dependent,
CVaR Deviation, CVaR Deviation Normal Independent, CVaR Deviation Normal Dependent,
CVaR for Mixture of Normal Independent, CVaR Deviation for Mixture of Normal Independent
CVaR for Discrete Distribution as Function of Atom Probabilities, CVaR for Mixture of Normal Distributions as Function of Mixture Weights