DiscreteLinearTradingEnhanced.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>DiscreteLinearTradingEnhanced</i> contains the Volatility Trading Trajectory generated by the Almgren
 * (2003) Scheme under the Criterion of No-Drift AND Linear Temporary Impact Volatility. 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. 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. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk
 *              <i>Applied Mathematical Finance</i> <b>10 (1)</b> 1-18
 *      </li>
 *      <li>
 *          Almgren, R., and N. Chriss (2003): Bidding Principles <i>Risk</i> 97-102
 *      </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>
 *  </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 DiscreteLinearTradingEnhanced extends org.drip.execution.nonadaptive.StaticOptimalSchemeDiscrete
{

    /**
     * Create the Standard DiscreteLinearTradingEnhanced Instance
     * 
     * @param dblStartHoldings Trajectory Start Holdings
     * @param dblFinishTime Trajectory Finish Time
     * @param iNumInterval The Number of Fixed Intervals
     * @param apep Almgren 2003 Arithmetic Price Evolution Parameters
     * @param dblRiskAversion The Risk Aversion Parameter
     * 
     * @return The DiscreteLinearTradingEnhanced Instance
     */

    public static final DiscreteLinearTradingEnhanced Standard (
        final double dblStartHoldings,
        final double dblFinishTime,
        final int iNumInterval,
        final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
        final double dblRiskAversion)
    {
        try {
            return new DiscreteLinearTradingEnhanced
                (org.drip.execution.strategy.DiscreteTradingTrajectoryControl.FixedInterval (new
                    org.drip.execution.strategy.OrderSpecification (dblStartHoldings, dblFinishTime),
                        iNumInterval), apep, new org.drip.execution.risk.MeanVarianceObjectiveUtility
                            (dblRiskAversion));
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    private DiscreteLinearTradingEnhanced (
        final org.drip.execution.strategy.DiscreteTradingTrajectoryControl dttc,
        final org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep,
        final org.drip.execution.risk.MeanVarianceObjectiveUtility mvou)
        throws java.lang.Exception
    {
        super (dttc, apep, mvou);
    }

    @Override public org.drip.execution.optimum.EfficientTradingTrajectory generate()
    {
        org.drip.execution.dynamics.ArithmeticPriceEvolutionParameters apep = priceEvolutionParameters();

        double dblLambda = ((org.drip.execution.risk.MeanVarianceObjectiveUtility)
            objectiveUtility()).riskAversion();

        double dblSigma = java.lang.Double.NaN;

        try {
            dblSigma = apep.arithmeticPriceDynamicsSettings().epochVolatility();
        } catch (java.lang.Exception e) {
            e.printStackTrace();

            return null;
        }

        org.drip.execution.impact.TransactionFunction tfTemporaryExpectation =
            apep.temporaryExpectation().epochImpactFunction();

        if (!(tfTemporaryExpectation instanceof org.drip.execution.impact.TransactionFunctionLinear))
            return null;

        org.drip.execution.impact.TransactionFunction tfTemporaryVolatility =
            apep.temporaryVolatility().epochImpactFunction();

        if (!(tfTemporaryVolatility instanceof org.drip.execution.impact.TransactionFunctionLinear))
            return null;

        double dblTStar = java.lang.Math.sqrt (((org.drip.execution.impact.TransactionFunctionLinear)
            tfTemporaryExpectation).slope() / (dblLambda * dblSigma * dblSigma));

        return org.drip.execution.optimum.TradingEnhancedDiscrete.Standard
            ((org.drip.execution.strategy.DiscreteTradingTrajectory) super.generate(), apep, dblTStar,
                dblSigma * dblTStar * dblTStar / ((org.drip.execution.impact.TransactionFunctionLinear)
                    tfTemporaryVolatility).slope() * java.lang.Math.sqrt (3.));
    }
}