NonDimensionalCostEvolver.java
package org.drip.execution.hjb;
/*
* -*- 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>NonDimensionalCostEvolver</i> exposes the HJB-based Single Step Optimal Trajectory Cost Step Evolver
* using the Variants of the Coordinated Variation Version of the Stochastic Volatility and the Transaction
* Function arising from the Realization of the Market State Variable as described in the "Trading Time"
* Model. The References are:
*
* <br><br>
* <ul>
* <li>
* Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
* Risk</i> <b>3 (2)</b> 5-39
* </li>
* <li>
* Almgren, R. F. (2009): Optimal Trading in a Dynamic Market
* https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
* </li>
* <li>
* Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility <i>SIAM Journal
* of Financial Mathematics</i> <b>3 (1)</b> 163-181
* </li>
* <li>
* Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes <i>Mathematical
* Finance</i> <b>11 (1)</b> 79-96
* </li>
* <li>
* Jones, C. M., G. Kaul, and M. L. Lipson (1994): Transactions, Volume, and Volatility <i>Review of
* Financial Studies</i> <b>7 (4)</b> 631-651
* </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/hjb/README.md">Hamilton Jacobin Bellman Based Optimal Evolution</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class NonDimensionalCostEvolver {
protected static final double SINGULAR_URGENCY_THRESHOLD = 50.;
private boolean _bAsymptoticEnhancedEulerCorrection = false;
private org.drip.measure.process.OrnsteinUhlenbeck _ou = null;
private double _dblAsymptoticEulerUrgencyThreshold = java.lang.Double.NaN;
protected abstract double advance (
final org.drip.execution.hjb.NonDimensionalCost ndc,
final org.drip.execution.latent.MarketState ms,
final double[] adblMarketStateTweak,
final double dblNonDimensionalRiskAversion)
throws java.lang.Exception;
protected NonDimensionalCostEvolver (
final org.drip.measure.process.OrnsteinUhlenbeck ou,
final double dblAsymptoticEulerUrgencyThreshold,
final boolean bAsymptoticEnhancedEulerCorrection)
throws java.lang.Exception
{
if (null == (_ou = ou) || !org.drip.numerical.common.NumberUtil.IsValid
(_dblAsymptoticEulerUrgencyThreshold = dblAsymptoticEulerUrgencyThreshold))
throw new java.lang.Exception ("NonDimensionalCostEvolver Constructor => Invalid Inputs");
_bAsymptoticEnhancedEulerCorrection = bAsymptoticEnhancedEulerCorrection;
}
/**
* Retrieve the Asymptotic Enhanced Euler Correction Application Flag
*
* @return The Asymptotic Enhanced Euler Correction Application Flag
*/
public boolean asymptoticEnhancedEulerCorrection()
{
return _bAsymptoticEnhancedEulerCorrection;
}
/**
* Retrieve the Asymptotic Euler Urgency Threshold
*
* @return The Asymptotic Euler Urgency Threshold
*/
public double asymptoticEulerUrgencyThreshold()
{
return _dblAsymptoticEulerUrgencyThreshold;
}
/**
* Retrieve the Reference Ornstein-Unlenbeck Process
*
* @return The Reference Ornstein-Unlenbeck Process
*/
public org.drip.measure.process.OrnsteinUhlenbeck ornsteinUnlenbeckProcess()
{
return _ou;
}
/**
* Evolve a Single Time Step of the Optimal Trajectory
*
* @param ndc The Initial Non Dimensional Cost Value Function
* @param ms The Market State
* @param dblNonDimensionalRiskAversion The Non Dimensional Risk Aversion Parameter
* @param dblNonDimensionalTime The Non Dimensional Time Node
* @param dblNonDimensionalTimeIncrement The Non Dimensional Time Increment
*
* @return The Post Evolved Non-dimensional Cost Value Function
*/
public abstract org.drip.execution.hjb.NonDimensionalCost evolve (
final org.drip.execution.hjb.NonDimensionalCost ndc,
final org.drip.execution.latent.MarketState ms,
final double dblNonDimensionalRiskAversion,
final double dblNonDimensionalTime,
final double dblNonDimensionalTimeIncrement);
}