StaticOptimalSchemeDiscrete.java
package org.drip.execution.nonadaptive;
/*
* -*- 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>StaticOptimalSchemeDiscrete</i> generates the Trade/Holdings List of Static Optimal Execution Schedule
* based on the Discrete Trade Trajectory Control, the Price Walk Parameters, and the Objective Utility
* Function. 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>
* Bertsimas, D., and A. W. Lo (1998): Optimal Control of Execution Costs <i>Journal of Financial
* Markets</i> <b>1</b> 1-50
* </li>
* <li>
* Chan, L. K. C., and J. Lakonishak (1995): The Behavior of Stock Prices around Institutional
* Trades <i>Journal of Finance</i> <b>50</b> 1147-1174
* </li>
* <li>
* Keim, D. B., and A. Madhavan (1997): Transaction Costs and Investment Style: An Inter-exchange
* Analysis of Institutional Equity Trades <i>Journal of Financial Economics</i> <b>46</b>
* 265-292
* </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/nonadaptive/README.md">Almgren-Chriss Static Optimal Trajectory</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class StaticOptimalSchemeDiscrete extends org.drip.execution.nonadaptive.StaticOptimalScheme {
private org.drip.execution.strategy.DiscreteTradingTrajectoryControl _dttc = null;
private double[] completeHoldings (
final double[] adblInnerHoldings)
{
if (null == adblInnerHoldings) return null;
int iNumCompleteHoldings = adblInnerHoldings.length + 2;
double[] adblCompleteHoldings = new double[iNumCompleteHoldings];
for (int i = 0; i < iNumCompleteHoldings; ++i) {
if (0 == i)
adblCompleteHoldings[i] = _dttc.startHoldings();
else if (iNumCompleteHoldings - 1 == i)
adblCompleteHoldings[i] = 0.;
else
adblCompleteHoldings[i] = adblInnerHoldings[i - 1];
}
return adblCompleteHoldings;
}
private org.drip.execution.sensitivity.ControlNodesGreek objectiveSensitivity (
final double[] adblInnerHoldings)
{
org.drip.execution.capture.TrajectoryShortfallEstimator tse = null;
try {
tse = new org.drip.execution.capture.TrajectoryShortfallEstimator
(org.drip.execution.strategy.DiscreteTradingTrajectory.Standard (_dttc.executionTimeNodes(),
completeHoldings (adblInnerHoldings)));
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep = priceEvolutionParameters();
org.drip.execution.sensitivity.ControlNodesGreek cngVariance = tse.varianceContribution (apep);
org.drip.execution.sensitivity.ControlNodesGreek cngExpectation = tse.expectationContribution (apep);
if (null == cngExpectation || null == cngVariance) return null;
return objectiveUtility().sensitivity ((org.drip.execution.sensitivity.TrajectoryControlNodesGreek)
cngExpectation, (org.drip.execution.sensitivity.TrajectoryControlNodesGreek) cngVariance);
}
private org.drip.function.definition.RdToR1 optimizerRdToR1()
{
return new org.drip.function.definition.RdToR1 (null) {
@Override public int dimension()
{
return _dttc.executionTimeNodes().length - 2;
}
@Override public double evaluate (
final double[] adblInnerHoldings)
throws java.lang.Exception
{
org.drip.execution.sensitivity.ControlNodesGreek cngObjectiveUtility = objectiveSensitivity
(adblInnerHoldings);
if (null == cngObjectiveUtility)
throw new java.lang.Exception
("StaticOptimalSchemeDiscrete::optimizerRdToR1::evaluate => Invalid Inputs");
return cngObjectiveUtility.value();
}
@Override public double[] jacobian (
final double[] adblInnerHoldings)
{
org.drip.execution.sensitivity.ControlNodesGreek cngObjectiveUtility = objectiveSensitivity
(adblInnerHoldings);
return null == cngObjectiveUtility ? null : cngObjectiveUtility.jacobian();
}
@Override public double[][] hessian (
final double[] adblInnerHoldings)
{
org.drip.execution.sensitivity.ControlNodesGreek cngObjectiveUtility = objectiveSensitivity
(adblInnerHoldings);
return null == cngObjectiveUtility ? null : cngObjectiveUtility.hessian();
}
};
}
/**
* StaticOptimalSchemeDiscrete Constructor
*
* @param dttc The Discrete Trading Trajectory Control Parameters
* @param apep The Arithmetic Price Walk Parameters
* @param ou The Optimizer Objective Utility Function
*
* @throws java.lang.Exception Thrown if the Inputs are not valid
*/
public StaticOptimalSchemeDiscrete (
final org.drip.execution.strategy.DiscreteTradingTrajectoryControl dttc,
final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
final org.drip.execution.risk.ObjectiveUtility ou)
throws java.lang.Exception
{
super (apep, ou);
if (null == (_dttc = dttc))
throw new java.lang.Exception ("StaticOptimalSchemeDiscrete Constructor => Invalid Inputs");
}
/**
* Retrieve the Discrete Trajectory Control Settings
*
* @return The Discrete Trajectory Control Settings
*/
public org.drip.execution.strategy.DiscreteTradingTrajectoryControl control()
{
return _dttc;
}
@Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
{
double[] adblExecutionTimeNode = _dttc.executionTimeNodes();
org.drip.execution.strategy.DiscreteTradingTrajectory dtt =
org.drip.execution.strategy.DiscreteTradingTrajectory.Linear (adblExecutionTimeNode,
_dttc.startHoldings(), 0.);
if (null == dtt) return null;
org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier vicm = null;
try {
if (null == (vicm = new org.drip.function.rdtor1solver.NewtonFixedPointFinder (optimizerRdToR1(),
null, org.drip.function.rdtor1solver.ConvergenceControl.Standard()).convergeVariate (new
org.drip.function.rdtor1solver.VariateInequalityConstraintMultiplier (false,
dtt.innerHoldings(), null))))
return null;
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
return org.drip.execution.optimum.EfficientTradingTrajectoryDiscrete.Standard (adblExecutionTimeNode,
completeHoldings (vicm.variateArray()), priceEvolutionParameters());
}
}