PowerVarianceObjectiveUtility.java
package org.drip.execution.risk;
/*
* -*- 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>PowerVarianceObjectiveUtility</i> implements the Mean-Power-Variance Objective Utility Function that
* needs to be optimized to extract the Optimal Execution Trajectory. The Exact Objective Function is of the
* Form:
*
* U[x] = E[x] + lambda * (V[x] ^p)
*
* where p is greater than 0.
*
* p = 1
*
* is the Regular Mean-Variance, and
*
* p = 0.5
*
* is VaR Minimization (L-VaR). The References are:
*
* <br><br>
* <ul>
* <li>
* Almgren, R., and N. Chriss (1999): Value under Liquidation <i>Risk</i> <b>12 (12)</b>
* </li>
* <li>
* Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
* Risk</i> <b>3 (2)</b> 5-39
* </li>
* <li>
* Almgren, R. (2003): Optimal Execution with Non-linear Impact Functions and Trading Enhanced Risk
* <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18
* </li>
* <li>
* Artzner, P., F. Delbaen, J. M. Eber, and D. Heath (1999): Coherent Measures of Risk
* <i>Mathematical Finance</i> <b>9</b> 203-228
* </li>
* <li>
* Basak, S., and A. Shapiro (2001): Value-at-Risk Based Risk Management: Optimal Policies and Asset
* Prices <i>Review of Financial Studies</i> <b>14</b> 371-405
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ProductCore.md">Product Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/TransactionCostAnalyticsLibrary.md">Transaction Cost Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/README.md">Optimal Impact/Capture Based Trading Trajectories - Deterministic, Stochastic, Static, and Dynamic</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/execution/risk/README.md">Optimal Execution MVO Efficient Frontier</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class PowerVarianceObjectiveUtility implements org.drip.execution.risk.ObjectiveUtility {
private double _dblRiskAversion = java.lang.Double.NaN;
private double _dblVarianceExponent = java.lang.Double.NaN;
/**
* Generate the Liquidity VaR Version of the Power Variance Utility Function
*
* @param dblRiskAversion The Risk Aversion Parameter
*
* @return The Liquidity VaR Version of the Power Variance Utility Function
*/
public static final PowerVarianceObjectiveUtility LiquidityVaR (
final double dblRiskAversion)
{
try {
return new PowerVarianceObjectiveUtility (0.5, dblRiskAversion);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* PowerVarianceObjectiveUtility Constructor
*
* @param dblVarianceExponent The Variance Exponent
* @param dblRiskAversion The Risk Aversion Parameter
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public PowerVarianceObjectiveUtility (
final double dblVarianceExponent,
final double dblRiskAversion)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblVarianceExponent = dblVarianceExponent) || 0. >
_dblVarianceExponent || !org.drip.numerical.common.NumberUtil.IsValid (_dblRiskAversion =
dblRiskAversion) || 0. > _dblRiskAversion)
throw new java.lang.Exception ("PowerVarianceObjectiveUtility Constructor => Invalid Inputs!");
}
/**
* Retrieve the Risk Aversion Parameter
*
* @return The Risk Aversion Parameter
*/
public double riskAversion()
{
return _dblRiskAversion;
}
/**
* Retrieve the Variance Exponent
*
* @return The Variance Exponent
*/
public double varianceExponent()
{
return _dblVarianceExponent;
}
@Override public org.drip.execution.sensitivity.ControlNodesGreek sensitivity (
final org.drip.execution.sensitivity.TrajectoryControlNodesGreek tcngExpectation,
final org.drip.execution.sensitivity.TrajectoryControlNodesGreek tcngVariance)
{
if (null == tcngExpectation || null == tcngVariance) return null;
double[] adblVarianceJacobian = tcngVariance.innerJacobian();
if (null == adblVarianceJacobian) return null;
double dblVarianceValue = tcngVariance.value();
double[][] aadblVarianceHessian = tcngVariance.innerHessian();
double[] adblExpectationJacobian = tcngExpectation.innerJacobian();
double[][] aadblExpectationHessian = tcngExpectation.innerHessian();
int iNumControlNode = adblVarianceJacobian.length;
double[] adblObjectiveJacobian = new double[iNumControlNode];
double[][] aadblObjectiveHessian = new double[iNumControlNode][iNumControlNode];
double dblJacobianMultiplier = _dblVarianceExponent * _dblRiskAversion * java.lang.Math.pow
(dblVarianceValue, _dblVarianceExponent - 1.);
double dblJacobianProductMultiplier = _dblVarianceExponent * (_dblVarianceExponent - 1.) *
_dblRiskAversion * java.lang.Math.pow (dblVarianceValue, _dblVarianceExponent - 2.);
for (int i = 0; i < iNumControlNode; ++i) {
adblObjectiveJacobian[i] = adblExpectationJacobian[i] + dblJacobianMultiplier *
adblVarianceJacobian[i];
for (int j = 0; j < iNumControlNode; ++j)
aadblObjectiveHessian[i][j] = aadblExpectationHessian[i][j] + dblJacobianProductMultiplier *
adblVarianceJacobian[i] * adblVarianceJacobian[j] + dblJacobianMultiplier *
aadblVarianceHessian[i][j];
}
try {
return new org.drip.execution.sensitivity.ControlNodesGreek (tcngExpectation.value() +
_dblRiskAversion * java.lang.Math.pow (dblVarianceValue, _dblVarianceExponent),
adblObjectiveJacobian, aadblObjectiveHessian);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}