Ulcer Index Constraints

PortfolioOptimisers.set_risk_constraints! Method

julia

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

Add Ulcer Index risk constraints to model.

Introduces a scalar variable uci and the SOC constraint [sc * uci; sc * dd[2:T+1]] in SecondOrderCone(), then defines uci_risk = uci / sqrt(T). Returns the existing expression if already present.

Mathematical definition

\begin{aligned} UCI (w) & = \frac{∥ d d ∥_{2}}{\sqrt{T}} = \sqrt{\frac{1}{T} \sum_{t = 1}^{T} d d_{t}^{2}} . \end{aligned}

Where:

$UCI (w)$ : Ulcer index.
$d d$ : Drawdown vector.
$T$ : Number of observations.
$d d_{t}$ : Portfolio drawdown at time $t$ .

where $d d_{t}$ is the portfolio drawdown at time $t$ .

Arguments

model::JuMP.Model: The JuMP optimisation model.
r::UlcerIndex: Ulcer index risk measure instance.
opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.
pr::AbstractPriorResult: Prior result containing the returns matrix X.

Returns

nothing.

Related

source

Ulcer Index Constraints ​

Ulcer Index Constraints