Worst Realisation Constraints: private API

set_wr_risk_expression!(
    model::Model,
    X::AbstractMatrix{<:Union{var"#s136", var"#s53"} where {var"#s136"<:Number, var"#s53"<:AbstractJuMPScalar}};
    loss,
    prefix
) -> Any

Introduce the worst-realisation risk variable and constraint to model.

Creates a scalar variable wr_risk and adds sc * (wr_risk .+ net_X) >= 0 so that wr_risk upper-bounds the negative of every portfolio return. Returns the existing variable if already present.

Mathematical definition

\[\begin{align} \mathrm{WR}(\boldsymbol{w}) &= \max_{t} (-\hat{r}_t) = -\min_{t} \hat{r}_t\,. \end{align}\]

Where:

• $\mathrm{WR}(\boldsymbol{w})$: Worst realisation.
• $\hat{r}_t = \boldsymbol{x}_t^\intercal \boldsymbol{w}$: Portfolio return at time $t$.

where $\hat{r}_t = \boldsymbol{x}_t^\intercal \boldsymbol{w}$ is the net portfolio return at time $t$.

Arguments

• model::JuMP.Model: The JuMP optimisation model.
• X::MatNum: Asset returns matrix (T × N).

Returns

• wr_risk: JuMP scalar variable for the worst-realisation risk.

Related

• set_risk_constraints!

set_risk_constraints!(
    model::Model,
    ,
    r::WorstRealisation,
    opt::RiskJuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    args...;
    loss,
    prefix,
    kwargs...
) -> Any

Add worst-realisation risk constraints to model.

Delegates to set_wr_risk_expression! to create wr_risk, then calls set_risk_bounds_and_expression!. Returns the existing expression if already present.

Arguments

• model::JuMP.Model: The JuMP optimisation model.
• r::WorstRealisation: Worst-realisation risk measure instance.
• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.
• pr::AbstractPriorResult: Prior result containing the returns matrix X.

Returns

• nothing.

Related

• set_wr_risk_expression!
• set_risk_bounds_and_expression!