org.akutan.optimization
Class UtilitySolver

java.lang.Object
  org.akutan.optimization.ActiveSetSolver
      org.akutan.optimization.UtilitySolver

All Implemented Interfaces:

Solver

public class UtilitySolver
extends ActiveSetSolver
implements Solver

Subclass of ActiveSetSolver that solves the mean variance portfolio optimization problem by minimizing the utility for a given risk aversion parameter. The utility function is the standard mean variance one.

Since:

3 Nov 2005

Field Summary

protected cern.colt.matrix.DoubleMatrix1D	_e_rx
protected cern.colt.matrix.DoubleMatrix2D	_V

Fields inherited from class org.akutan.optimization.ActiveSetSolver

df

Constructor Summary

UtilitySolver(cern.colt.matrix.DoubleMatrix1D e_r, cern.colt.matrix.DoubleMatrix2D V_p)
Constructs the solver

Method Summary

java.util.List<SolvedPoint>	solve(java.util.List<Constraint> extraConstraints, org.akutan.optimization.ProgressIndicator progress) Called to return a list of points on the efficient frontier.
SolvedPoint	solveSingle(double lambda, cern.colt.matrix.DoubleMatrix1D e_rx, cern.colt.matrix.DoubleMatrix2D Vx, java.util.List<Constraint> constraints, java.util.Set<java.lang.Integer> equality, java.util.Set<java.lang.Integer> active, java.util.Set<java.lang.Integer> inactive) Active set code to optimize a single portfolio for a fixed return

Methods inherited from class org.akutan.optimization.ActiveSetSolver

algorithm, dumpConstraints, formatOutput, generateConstraints, generateValues, initialGuess, make2D, makePoint, setMatrix, setMatrix, solve, solveSingle

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

_e_rx

protected cern.colt.matrix.DoubleMatrix1D _e_rx

_V

protected cern.colt.matrix.DoubleMatrix2D _V

Constructor Detail

UtilitySolver

public UtilitySolver(cern.colt.matrix.DoubleMatrix1D e_r,
                     cern.colt.matrix.DoubleMatrix2D V_p)

Constructs the solver

Parameters:

e_r - Vector of Expected returns

V_p - Covariance matrix

Method Detail

solve

public java.util.List<SolvedPoint> solve(java.util.List<Constraint> extraConstraints,
                                         org.akutan.optimization.ProgressIndicator progress)

Called to return a list of points on the efficient frontier. Adds no short positions and budget constraints to the problem specified by the client.

Specified by:

solve in interface Solver

Parameters:

extraConstraints - Additional constraints applied by the client

Returns:

An ordered list of points on the efficient frontier, ordered from high risk to low risk.

solveSingle

public SolvedPoint solveSingle(double lambda,
                               cern.colt.matrix.DoubleMatrix1D e_rx,
                               cern.colt.matrix.DoubleMatrix2D Vx,
                               java.util.List<Constraint> constraints,
                               java.util.Set<java.lang.Integer> equality,
                               java.util.Set<java.lang.Integer> active,
                               java.util.Set<java.lang.Integer> inactive)

Active set code to optimize a single portfolio for a fixed return

Parameters:

lambda - Parameter which scales the risk aversion, but is specified linearly

e_rx - Expected returns vector

Vx - Covariance matrix

constraints - List of constraints

equality - Set of equality constraints

active - Set of initially active inequality constraints

inactive - Set of initially inactive inequality constraints

Returns:

The single point while has the maximum utility for this level of risk aversion