Package dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization

Class PortfolioRiskExactSigma

java.lang.Object
dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPPortfolioConstraint
dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.SOCPRiskConstraint
dev.nm.solver.multivariate.constrained.convex.sdp.socp.problem.portfoliooptimization.PortfolioRiskExactSigma
All Implemented Interfaces:
Function<Vector,Double>, RealScalarFunction
public class PortfolioRiskExactSigma extends SOCPRiskConstraint
Constructs the constraint coefficient arrays of the portfolio risk term in the compact form. The constraints are generated during the transformation of the objective function.

The portfolio risk in the objective function is transformed into the following constraints: \[ (x+w^{0})^{\top}\Sigma(x+w^{0})\leq t_1. \] By letting \(y=x+w^{0}\), it can be written as: \[ y^{\top}\Sigma\;y\leq t_1 \] When the exact covariance matrix \(\Sigma\) is used, then the portfolio risk constraint is equivalent to: \[ y^{\top}\Sigma\;y\leq t_1 \Longleftrightarrow y^{\top}\Sigma\;y+(\frac{t_{1}-1}{2})^{2}\leq(\frac{t_{1}+1}{2})^{2}\Longleftrightarrow ||\left(\begin{array}{c}\Sigma^{\frac{1}{2}}y\\\frac{t_{1}-1}{2}\end{array}\right)||_{2}\leq \frac{t_{1}+1}{2}. \] And the standard SOCP form of the portfolio risk constraint in this case are: \[ ||\left(\begin{array}{c}\Sigma^{\frac{1}{2}}y\\\frac{t_{1}-1}{2}\end{array}\right)||_{2}\leq \frac{t_{1}+1}{2}\Longleftrightarrow ||A_{1}^{\top}z+C_{1}||_{2}\leq b^{\top}_{1}z+d_{1}\\ A_{1}^{\top}=\left(\begin{array}{cc}\Sigma^{\frac{1}{2}} invalid input: '&' 0_{n\times 1}\\0_{1\times n} invalid input: '&' 1/2\end{array}\right)\nonumber,\; C_{1}=\left(\begin{array}{c}0_{n\times 1}\\-1/2\end{array}\right),\; b_{1}=\left(\begin{array}{c}0_{n\times 1}\\1/2\end{array}\right)\; d_{1}=\frac{1}{2},\; z=\left(\begin{array}{c}y\\t_{1}\end{array}\right). \]

  • Constructor Details

    • PortfolioRiskExactSigma

      public PortfolioRiskExactSigma(Matrix Sigma, PortfolioRiskExactSigma.MatrixRoot root)
      Transforms the portfolio risk term, \(y^{\top}\Sigma\;y\leq t_1\), into the standard SOCP form when the exact covariance matrix is used.
      Parameters:
      Sigma - the covariance matrix
      root - the method to compute the root of a matrix

    • PortfolioRiskExactSigma

      public PortfolioRiskExactSigma(Matrix Sigma, Matrix sigmaRoot)
      Transforms the portfolio risk term, \(y^{\top}\Sigma\;y\leq t_1\), into the standard SOCP form when the exact covariance matrix is used.
      Parameters:
      Sigma - the covariance matrix
      sigmaRoot - the root of a matrix

    • PortfolioRiskExactSigma

      public PortfolioRiskExactSigma(Matrix Sigma)
      Transforms the portfolio risk term, \(y^{\top}\Sigma\;y\leq t_1\), into the standard SOCP form when the exact covariance matrix is used.
      Parameters:
      Sigma - the covariance matrix

  • Method Details

    • Sigma

      public Matrix Sigma()
      Specified by:
      Sigma in class SOCPRiskConstraint

    • root

      public Matrix root()

    • areAllConstraintsSatisfied

      public boolean areAllConstraintsSatisfied(Vector y)
      Checks whether all SOCP constraints represented by this portfolio constraint are satisfied. The constraint generated by objective function to find the optimal solution. It cannot be "violated".
      Specified by:
      areAllConstraintsSatisfied in class SOCPPortfolioConstraint
      Parameters:
      y - a portfolio solution or allocation; the asset weights
      Returns:
      true

    • evaluate

      public Double evaluate(Vector y)
      Description copied from interface: Function
      Evaluate the function f at x, where x is from the domain.
      Parameters:
      y - x
      Returns:
      f(x)

    • dimensionOfDomain

      public int dimensionOfDomain()
      Description copied from interface: Function
      Get the number of variables the function has. For example, for a univariate function, the domain dimension is 1; for a bivariate function, the domain dimension is 2.
      Returns:
      the number of variables

    • dimensionOfRange

      public int dimensionOfRange()
      Description copied from interface: Function
      Get the dimension of the range space of the function. For example, for a Rn->Rm function, the dimension of the range is m.
      Returns:
      the dimension of the range