DualConstrainedEllipsoidVariance.java

package org.drip.sample.semidefinite;

import org.drip.function.definition.RdToR1;
import org.drip.function.rdtor1.*;
import org.drip.function.rdtor1descent.LineStepEvolutionControl;
import org.drip.function.rdtor1solver.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * 
 *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
 *      libraries targeting analysts and developers
 *      https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *      Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *      you may not use this file except in compliance with the License.
 *   
 *  You may obtain a copy of the License at
 *      http://www.apache.org/licenses/LICENSE-2.0
 *  
 *  Unless required by applicable law or agreed to in writing, software
 *      distributed under the License is distributed on an "AS IS" BASIS,
 *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  
 *  See the License for the specific language governing permissions and
 *      limitations under the License.
 */

/**
 * DualConstrainedEllipsoidVariance demonstrates the Application of the Interior Point Method for Minimizing
 *  the Variance Across The Specified Ellipsoid under both Normalization and first Moment Constraints.
 *
 * @author Lakshmi Krishnamurthy
 */

public class DualConstrainedEllipsoidVariance
{

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv ("");

        String[] entityNameArray = new String[]
        {
            "IBM",
            "ATT",
            "ALU",
            "QCO",
            "INT",
            "MSF",
            "VER"
        };
        double[] entityReturnsArray = new double[]
        {
            0.0264,
            0.0332,
            0.0400,
            0.0468,
            0.0536,
            0.0604,
            0.0672
        };
        double entityDesignReturn = 0.0468;
        double[][] entityCovarianceMatrix = new double[][]
        {
            {1.00, 0.76, 0.80, 0.38, 0.60, 0.61, 0.51},
            {0.76, 1.00, 0.65, 0.35, 0.56, 0.43, 0.40},
            {0.80, 0.65, 1.00, 0.68, 0.74, 0.40, 0.51},
            {0.38, 0.35, 0.68, 1.00, 0.72, 0.02, 0.57},
            {0.60, 0.56, 0.74, 0.72, 1.00, 0.31, 0.67},
            {0.61, 0.43, 0.40, 0.02, 0.31, 1.00, 0.39},
            {0.51, 0.40, 0.51, 0.57, 0.67, 0.39, 1.00}
        };

        InteriorPointBarrierControl interiorPointBarrierControl = InteriorPointBarrierControl.Standard();

        System.out.println ("\n\n\t|------------------------------------------------------||");

        String header = "\t|     |";

        for (int entityIndex = 0;
            entityIndex < entityNameArray.length;
            ++entityIndex)
        {
            header += " " + entityNameArray[entityIndex] + "  |";
        }

        System.out.println (header + "|");

        System.out.println ("\t|------------------------------------------------------||");

        for (int entityIndexI = 0;
            entityIndexI < entityNameArray.length;
            ++entityIndexI)
        {
            String dump = "\t| " + entityNameArray[entityIndexI] + " ";

            for (int entityIndexJ = 0;
                entityIndexJ < entityNameArray.length;
                ++entityIndexJ)
            {
                dump += "|" + FormatUtil.FormatDouble (
                    entityCovarianceMatrix[entityIndexI][entityIndexJ], 1, 2, 1.
                ) + " ";
            }

            System.out.println (dump + "||");
        }

        System.out.println ("\t|------------------------------------------------------||\n\n");

        double equalityConstraintConstant = -1.;
        int entityCount = entityCovarianceMatrix.length;

        RdToR1[] equalityConstraintFunctionArray = new RdToR1[]
        {
            new AffineMultivariate (
                ObjectiveConstraintVariateSet.Unitary (
                    entityCount
                ),
                equalityConstraintConstant
            ),
            new AffineMultivariate (
                entityReturnsArray,
                -1. * entityDesignReturn
            )
        };

        int equalityConstraintCount = equalityConstraintFunctionArray.length;

        LagrangianMultivariate lagrangianMultivariate = new LagrangianMultivariate (
            new CovarianceEllipsoidMultivariate (
                entityCovarianceMatrix
            ),
            equalityConstraintFunctionArray
        );

        double[] optimalVariateArray = new BarrierFixedPointFinder (
            lagrangianMultivariate,
            new RdToR1[]
            {
                new AffineBoundMultivariate (
                    false,
                    0,
                    entityCount + equalityConstraintCount,
                    0.05
                ),
                new AffineBoundMultivariate (
                    true,
                    0,
                    entityCount + equalityConstraintCount,
                    0.65
                ),
                new AffineBoundMultivariate (false, 1, entityCount + equalityConstraintCount, 0.05),
                new AffineBoundMultivariate (true, 1, entityCount + equalityConstraintCount, 0.65),
                new AffineBoundMultivariate (false, 2, entityCount + equalityConstraintCount, 0.05),
                new AffineBoundMultivariate (true, 2, entityCount + equalityConstraintCount, 0.65),
                new AffineBoundMultivariate (false, 3, entityCount + equalityConstraintCount, 0.05),
                new AffineBoundMultivariate (true, 3, entityCount + equalityConstraintCount, 0.65),
                new AffineBoundMultivariate (false, 4, entityCount + equalityConstraintCount, 0.05),
                new AffineBoundMultivariate (true, 4, entityCount + equalityConstraintCount, 0.65),
                new AffineBoundMultivariate (false, 5, entityCount + equalityConstraintCount, 0.05),
                new AffineBoundMultivariate (true, 5, entityCount + equalityConstraintCount, 0.65),
                new AffineBoundMultivariate (false, 6, entityCount + equalityConstraintCount, 0.05),
                new AffineBoundMultivariate (true, 6, entityCount + equalityConstraintCount, 0.65)
            },
            interiorPointBarrierControl,
            LineStepEvolutionControl.NocedalWrightStrongWolfe (
                false
            )
        ).solve (
            ObjectiveConstraintVariateSet.Uniform (
                entityCount,
                lagrangianMultivariate.constraintFunctionDimension()
            )
        ).variateArray();

        System.out.println ("\t|----------------------||");

        System.out.println ("\t|   OPTIMAL ENTITIES   ||");

        System.out.println ("\t|----------------------||");

        double expectedReturn = 0.;

        for (int entityIndex = 0;
            entityIndex < entityCount;
            ++entityIndex)
        {
            System.out.println (
                "\t|   " + entityNameArray[entityIndex] + "   =>  " + FormatUtil.FormatDouble (
                    optimalVariateArray[entityIndex], 2, 2, 100.
                ) + "%  ||"
            );

            expectedReturn += optimalVariateArray[entityIndex] * entityReturnsArray[entityIndex];
        }

        System.out.println ("\t|----------------------||\n");

        System.out.println ("\t|------------------------------||");

        System.out.println (
            "\t| DESIGN RETURN    => " + FormatUtil.FormatDouble (
                entityDesignReturn, 1, 5, 1.
            ) + " ||"
        );

        System.out.println (
            "\t| EXPECTED RETURN  => " + FormatUtil.FormatDouble (
                expectedReturn, 1, 5, 1.
            ) + " ||"
        );

        System.out.println (
            "\t| OPTIMAL VARIANCE => " + FormatUtil.FormatDouble (
                lagrangianMultivariate.evaluate (
                    optimalVariateArray
                ), 1, 5, 1.
            ) + " ||"
        );

        System.out.println ("\t|------------------------------||\n");
    }
}