RiskObjectiveUtilityMultivariate.java
package org.drip.function.rdtor1;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* 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.
*/
/**
* <i>RiskObjectiveUtilityMultivariate</i> implements the Risk Objective R<sup>d</sup> To R<sup>1</sup>
* Multivariate Function used in Portfolio Allocation. It accommodates both the Risk Tolerance and Risk
* Aversion Variants.
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <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>
* <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>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class RiskObjectiveUtilityMultivariate extends org.drip.function.definition.RdToR1 {
private double[] _adblExpectedReturns = null;
private double[][] _aadblCovarianceMatrix = null;
private double _dblRiskFreeRate = java.lang.Double.NaN;
private double _dblRiskAversion = java.lang.Double.NaN;
private double _dblRiskTolerance = java.lang.Double.NaN;
/**
* RiskObjectiveUtilityMultivariate Constructor
*
* @param aadblCovarianceMatrix The Co-variance Matrix Double Array
* @param adblExpectedReturns Array of Expected Returns
* @param dblRiskAversion The Risk Aversion Parameter
* @param dblRiskTolerance The Risk Tolerance Parameter
* @param dblRiskFreeRate The Risk Free Rate
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public RiskObjectiveUtilityMultivariate (
final double[][] aadblCovarianceMatrix,
final double[] adblExpectedReturns,
final double dblRiskAversion,
final double dblRiskTolerance,
final double dblRiskFreeRate)
throws java.lang.Exception
{
super (null);
if (null == (_aadblCovarianceMatrix = aadblCovarianceMatrix) || null == (_adblExpectedReturns =
adblExpectedReturns) || !org.drip.numerical.common.NumberUtil.IsValid (_dblRiskAversion =
dblRiskAversion) || !org.drip.numerical.common.NumberUtil.IsValid (_dblRiskTolerance =
dblRiskTolerance) || !org.drip.numerical.common.NumberUtil.IsValid (_dblRiskFreeRate =
dblRiskFreeRate))
throw new java.lang.Exception ("RiskObjectiveUtilityMultivariate Constructor => Invalid Inputs");
int iSize = _aadblCovarianceMatrix.length;
if (0 == iSize || iSize != _adblExpectedReturns.length)
throw new java.lang.Exception ("RiskObjectiveUtilityMultivariate Constructor => Invalid Inputs");
for (int i = 0; i < iSize; ++i) {
if (null == _aadblCovarianceMatrix[i] || iSize != _aadblCovarianceMatrix[i].length ||
!org.drip.numerical.common.NumberUtil.IsValid (_aadblCovarianceMatrix[i]) ||
!org.drip.numerical.common.NumberUtil.IsValid (_adblExpectedReturns[i]))
throw new java.lang.Exception
("RiskObjectiveUtilityMultivariate Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Input Variate Dimension
*
* @return The Input Variate Dimension
*/
public int dimension()
{
return _aadblCovarianceMatrix.length;
}
/**
* Retrieve the Co-variance Matrix
*
* @return The Co-variance Matrix
*/
public double[][] covariance()
{
return _aadblCovarianceMatrix;
}
/**
* Retrieve the Array of Expected Returns
*
* @return The Array of Expected Returns
*/
public double[] expectedReturns()
{
return _adblExpectedReturns;
}
/**
* Retrieve the Risk Aversion Factor
*
* @return The Risk Aversion Factor
*/
public double riskAversion()
{
return _dblRiskAversion;
}
/**
* Retrieve the Risk Tolerance Factor
*
* @return The Risk Tolerance Factor
*/
public double riskTolerance()
{
return _dblRiskTolerance;
}
/**
* Retrieve the Risk Free Rate
*
* @return The Risk Free Rate
*/
public double riskFreeRate()
{
return _dblRiskFreeRate;
}
@Override public double evaluate (
final double[] adblVariate)
throws java.lang.Exception
{
if (null == adblVariate || !org.drip.numerical.common.NumberUtil.IsValid (adblVariate))
throw new java.lang.Exception ("RiskObjectiveUtilityMultivariate::evaluate => Invalid Inputs");
double dblValue = 0.;
int iDimension = adblVariate.length;
if (iDimension != dimension())
throw new java.lang.Exception ("RiskObjectiveUtilityMultivariate::evaluate => Invalid Inputs");
for (int i = 0; i < iDimension; ++i) {
dblValue -= _dblRiskTolerance * adblVariate[i] * (_adblExpectedReturns[i] - _dblRiskFreeRate);
for (int j = 0; j < iDimension; ++j)
dblValue += 0.5 * _dblRiskAversion * adblVariate[i] * _aadblCovarianceMatrix[i][j] *
adblVariate[j];
}
return dblValue;
}
@Override public double[] jacobian (
final double[] adblVariate)
{
if (null == adblVariate || !org.drip.numerical.common.NumberUtil.IsValid (adblVariate)) return null;
int iDimension = adblVariate.length;
double[] adblJacobian = new double[iDimension];
if (iDimension != dimension()) return null;
for (int i = 0; i < iDimension; ++i) {
adblJacobian[i] = -1. * _dblRiskTolerance * (_adblExpectedReturns[i] - _dblRiskFreeRate);
for (int j = 0; j < iDimension; ++j)
adblJacobian[i] += _dblRiskAversion * _aadblCovarianceMatrix[i][j] * adblVariate[j];
}
return adblJacobian;
}
@Override public double[][] hessian (
final double[] adblVariate)
{
int iDimension = dimension();
double[][] aadblHessian = new double[iDimension][iDimension];
for (int i = 0; i < iDimension; ++i) {
for (int j = 0; j < iDimension; ++j)
aadblHessian[i][j] += _dblRiskAversion * _aadblCovarianceMatrix[i][j];
}
return aadblHessian;
}
}