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与之合作'Conditional'BoundType,MinNumAssets， 和MaxNumAssetsConstraints Using PortfolioCVaR Objects

When any one, or any combination of'Conditional'BoundType,MinNumAssets, orMaxNumAssetsconstraints are active, the portfolio problem is formulated by addingNumAssetsbinary variables, where0indicates not invested, and1投资。例如，解释'Conditional'BoundType和MinNumAssets和MaxNumAssetsconstraints, assume that your portfolio has a universe of 100 assets that you want to invest:

  • 'Conditional'BoundType（也称为半连续约束），由setBounds，通常在您不想投资少量价值的情况下使用。一个标准的例子是一个投资组合优化问题，由于交易成本，许多小型分配没有吸引力。取而代之的是，您更喜欢投资组合中使用较大分配的乐器。可以使用这种情况来处理'Conditional'BoundTypeconstraints for aPortfolioCVaR目的。

    For example, the weight you invest in each asset is either0或者between[0.01, 0.5]。Generally, a semicontinuous variablexis a continuous variable between bounds [磅,ub] that also can assume the value0, where磅>0,磅≤ub。将其应用于投资组合优化需要避免非常小或大的位置，即落入的值（0,磅) or are more thanub。

  • MinNumAssets和MaxNumAssets（也称为基数约束），由setminmaxnumassets, limit the number of assets in aPortfolioCVaR目的。For example, if you have 100 assets in your portfolio and you want the number of assets allocated in the portfolio to be from 40 through 60. UsingMinNumAssets和MaxNumAssets您可以限制优化投资组合中的资产数量，这使您可以限制交易和运营成本或创建索引跟踪投资组合。

环境'Conditional'BoundTypeConstraints Using thesetBounds功能

UsesetBoundswith a'conditional'BoundTypeto setxi=0或者0.02<=xi<=0.5for alli=1,...NumAssets:

p = PortfolioCVaR; p = setBounds(p, 0.02, 0.5,'BoundType','Conditional','NumAssets', 3)
p = PortfolioCVaR with properties: BuyCost: [] SellCost: [] RiskFreeRate: [] ProbabilityLevel: [] Turnover: [] BuyTurnover: [] SellTurnover: [] NumScenarios: [] Name: [] NumAssets: 3 AssetList: [] InitPort: [] AInequality: [] bInequality: [] AEquality: [] bEquality: [] LowerBound: [3×1 double] UpperBound: [3×1 double] LowerBudget: [] UpperBudget: [] GroupMatrix: [] LowerGroup: [] UpperGroup: [] GroupA: [] GroupB: [] LowerRatio: [] UpperRatio: [] MinNumAssets: [] MaxNumAssets: [] BoundType: [3×1 categorical]

环境the Limits on the Number of Assets Invested Using thesetminmaxnumassets功能

您也可以设置MinNumAssets和MaxNumAssetsproperties to define a limit on the number of assets invested usingsetminmaxnumassets。For example, by settingMinNumAssets=MaxNumAssets=2，这三个资产中只有两个投资于投资组合。

p = PortfolioCVaR; p = setBounds(p, 0.02, 0.5,'BoundType','Conditional','NumAssets'，3）p = setminmaxnumassets（p，2，2）
p = PortfolioCVaR with properties: BuyCost: [] SellCost: [] RiskFreeRate: [] ProbabilityLevel: [] Turnover: [] BuyTurnover: [] SellTurnover: [] NumScenarios: [] Name: [] NumAssets: 3 AssetList: [] InitPort: [] AInequality: [] bInequality: [] AEquality: [] bEquality: [] LowerBound: [3×1 double] UpperBound: [3×1 double] LowerBudget: [] UpperBudget: [] GroupMatrix: [] LowerGroup: [] UpperGroup: [] GroupA: [] GroupB: [] LowerRatio: [] UpperRatio: [] MinNumAssets: 2 MaxNumAssets: 2 BoundType: [3×1 categorical]

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