RiskObjectiveUtilityMultivariate.java

  1. package org.drip.function.rdtor1;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * 
  14.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  15.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  16.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  17.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  18.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  19.  *      and computational support.
  20.  *  
  21.  *      https://lakshmidrip.github.io/DROP/
  22.  *  
  23.  *  DROP is composed of three modules:
  24.  *  
  25.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  26.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  27.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  28.  * 
  29.  *  DROP Product Core implements libraries for the following:
  30.  *  - Fixed Income Analytics
  31.  *  - Loan Analytics
  32.  *  - Transaction Cost Analytics
  33.  * 
  34.  *  DROP Portfolio Core implements libraries for the following:
  35.  *  - Asset Allocation Analytics
  36.  *  - Asset Liability Management Analytics
  37.  *  - Capital Estimation Analytics
  38.  *  - Exposure Analytics
  39.  *  - Margin Analytics
  40.  *  - XVA Analytics
  41.  * 
  42.  *  DROP Computational Core implements libraries for the following:
  43.  *  - Algorithm Support
  44.  *  - Computation Support
  45.  *  - Function Analysis
  46.  *  - Model Validation
  47.  *  - Numerical Analysis
  48.  *  - Numerical Optimizer
  49.  *  - Spline Builder
  50.  *  - Statistical Learning
  51.  * 
  52.  *  Documentation for DROP is Spread Over:
  53.  * 
  54.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  55.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  56.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  57.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  58.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  59.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  60.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  61.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  62.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  63.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  64.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  65.  * 
  66.  *  Licensed under the Apache License, Version 2.0 (the "License");
  67.  *      you may not use this file except in compliance with the License.
  68.  *   
  69.  *  You may obtain a copy of the License at
  70.  *      http://www.apache.org/licenses/LICENSE-2.0
  71.  *  
  72.  *  Unless required by applicable law or agreed to in writing, software
  73.  *      distributed under the License is distributed on an "AS IS" BASIS,
  74.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  75.  *  
  76.  *  See the License for the specific language governing permissions and
  77.  *      limitations under the License.
  78.  */

  80. /**
  81.  * <i>RiskObjectiveUtilityMultivariate</i> implements the Risk Objective R<sup>d</sup> To R<sup>1</sup>
  82.  * Multivariate Function used in Portfolio Allocation. It accommodates both the Risk Tolerance and Risk
  83.  * Aversion Variants.
  84.  *
  85.  *  <br><br>
  86.  *  <ul>
  87.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  88.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  89.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/README.md">R<sup>d</sup> To R<sup>d</sup> Function Analysis</a></li>
  90.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/function/rdtor1/README.md">Built-in R<sup>d</sup> To R<sup>1</sup> Functions</a></li>
  91.  *  </ul>
  92.  *
  93.  * @author Lakshmi Krishnamurthy
  94.  */

  96. public class RiskObjectiveUtilityMultivariate extends org.drip.function.definition.RdToR1 {
  97.     private double[] _adblExpectedReturns = null;
  98.     private double[][] _aadblCovarianceMatrix = null;
  99.     private double _dblRiskFreeRate = java.lang.Double.NaN;
  100.     private double _dblRiskAversion = java.lang.Double.NaN;
  101.     private double _dblRiskTolerance = java.lang.Double.NaN;

  103.     /**
  104.      * RiskObjectiveUtilityMultivariate Constructor
  105.      * 
  106.      * @param aadblCovarianceMatrix The Co-variance Matrix Double Array
  107.      * @param adblExpectedReturns Array of Expected Returns
  108.      * @param dblRiskAversion The Risk Aversion Parameter
  109.      * @param dblRiskTolerance The Risk Tolerance Parameter
  110.      * @param dblRiskFreeRate The Risk Free Rate
  111.      * 
  112.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  113.      */

  115.     public RiskObjectiveUtilityMultivariate (
  116.         final double[][] aadblCovarianceMatrix,
  117.         final double[] adblExpectedReturns,
  118.         final double dblRiskAversion,
  119.         final double dblRiskTolerance,
  120.         final double dblRiskFreeRate)
  121.         throws java.lang.Exception
  122.     {
  123.         super (null);

  125.         if (null == (_aadblCovarianceMatrix = aadblCovarianceMatrix) || null == (_adblExpectedReturns =
  126.             adblExpectedReturns) || !org.drip.numerical.common.NumberUtil.IsValid (_dblRiskAversion =
  127.                 dblRiskAversion) || !org.drip.numerical.common.NumberUtil.IsValid (_dblRiskTolerance =
  128.                     dblRiskTolerance) || !org.drip.numerical.common.NumberUtil.IsValid (_dblRiskFreeRate =
  129.                         dblRiskFreeRate))
  130.             throw new java.lang.Exception ("RiskObjectiveUtilityMultivariate Constructor => Invalid Inputs");

  132.         int iSize = _aadblCovarianceMatrix.length;

  134.         if (0 == iSize || iSize != _adblExpectedReturns.length)
  135.             throw new java.lang.Exception ("RiskObjectiveUtilityMultivariate Constructor => Invalid Inputs");

  137.         for (int i = 0; i < iSize; ++i) {
  138.             if (null == _aadblCovarianceMatrix[i] || iSize != _aadblCovarianceMatrix[i].length ||
  139.                 !org.drip.numerical.common.NumberUtil.IsValid (_aadblCovarianceMatrix[i]) ||
  140.                     !org.drip.numerical.common.NumberUtil.IsValid (_adblExpectedReturns[i]))
  141.                 throw new java.lang.Exception
  142.                     ("RiskObjectiveUtilityMultivariate Constructor => Invalid Inputs");
  143.         }
  144.     }

  146.     /**
  147.      * Retrieve the Input Variate Dimension
  148.      * 
  149.      * @return The Input Variate Dimension
  150.      */

  152.     public int dimension()
  153.     {
  154.         return _aadblCovarianceMatrix.length;
  155.     }

  157.     /**
  158.      * Retrieve the Co-variance Matrix
  159.      * 
  160.      * @return The Co-variance Matrix
  161.      */

  163.     public double[][] covariance()
  164.     {
  165.         return _aadblCovarianceMatrix;
  166.     }

  168.     /**
  169.      * Retrieve the Array of Expected Returns
  170.      * 
  171.      * @return The Array of Expected Returns
  172.      */

  174.     public double[] expectedReturns()
  175.     {
  176.         return _adblExpectedReturns;
  177.     }

  179.     /**
  180.      * Retrieve the Risk Aversion Factor
  181.      * 
  182.      * @return The Risk Aversion Factor
  183.      */

  185.     public double riskAversion()
  186.     {
  187.         return _dblRiskAversion;
  188.     }

  190.     /**
  191.      * Retrieve the Risk Tolerance Factor
  192.      * 
  193.      * @return The Risk Tolerance Factor
  194.      */

  196.     public double riskTolerance()
  197.     {
  198.         return _dblRiskTolerance;
  199.     }

  201.     /**
  202.      * Retrieve the Risk Free Rate
  203.      * 
  204.      * @return The Risk Free Rate
  205.      */

  207.     public double riskFreeRate()
  208.     {
  209.         return _dblRiskFreeRate;
  210.     }

  212.     @Override public double evaluate (
  213.         final double[] adblVariate)
  214.         throws java.lang.Exception
  215.     {
  216.         if (null == adblVariate || !org.drip.numerical.common.NumberUtil.IsValid (adblVariate))
  217.             throw new java.lang.Exception ("RiskObjectiveUtilityMultivariate::evaluate => Invalid Inputs");

  219.         double dblValue = 0.;
  220.         int iDimension = adblVariate.length;

  222.         if (iDimension != dimension())
  223.             throw new java.lang.Exception ("RiskObjectiveUtilityMultivariate::evaluate => Invalid Inputs");

  225.         for (int i = 0; i < iDimension; ++i) {
  226.             dblValue -= _dblRiskTolerance * adblVariate[i] * (_adblExpectedReturns[i] - _dblRiskFreeRate);

  228.             for (int j = 0; j < iDimension; ++j)
  229.                 dblValue += 0.5 * _dblRiskAversion * adblVariate[i] * _aadblCovarianceMatrix[i][j] *
  230.                     adblVariate[j];
  231.         }

  233.         return dblValue;
  234.     }

  236.     @Override public double[] jacobian (
  237.         final double[] adblVariate)
  238.     {
  239.         if (null == adblVariate || !org.drip.numerical.common.NumberUtil.IsValid (adblVariate)) return null;

  241.         int iDimension = adblVariate.length;
  242.         double[] adblJacobian = new double[iDimension];

  244.         if (iDimension != dimension()) return null;

  246.         for (int i = 0; i < iDimension; ++i) {
  247.             adblJacobian[i] = -1. * _dblRiskTolerance * (_adblExpectedReturns[i] - _dblRiskFreeRate);

  249.             for (int j = 0; j < iDimension; ++j)
  250.                 adblJacobian[i] += _dblRiskAversion * _aadblCovarianceMatrix[i][j] * adblVariate[j];
  251.         }

  253.         return adblJacobian;
  254.     }

  256.     @Override public double[][] hessian (
  257.         final double[] adblVariate)
  258.     {
  259.         int iDimension = dimension();

  261.         double[][] aadblHessian = new double[iDimension][iDimension];

  263.         for (int i = 0; i < iDimension; ++i) {
  264.             for (int j = 0; j < iDimension; ++j)
  265.                 aadblHessian[i][j] += _dblRiskAversion * _aadblCovarianceMatrix[i][j];
  266.         }

  268.         return aadblHessian;
  269.     }
  270. }
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