PriorDriftDistribution.java

package org.drip.execution.bayesian;

/*
 * -*- 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>PriorDriftDistribution</i> holds the Prior Belief Distribution associated with the Directional Drift.
 * The References are:
 * 
 * <br><br>
 *  <ul>
 *      <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>
 *          Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions <i>Journal of
 *              Risk</i> <b>3 (2)</b> 5-39
 *      </li>
 *      <li>
 *          Brunnermeier, L. K., and L. H. Pedersen (2005): Predatory Trading <i>Journal of Finance</i> <b>60
 *              (4)</b> 1825-1863
 *      </li>
 *      <li>
 *          Almgren, R., and J. Lorenz (2006): Bayesian Adaptive Trading with a Daily Cycle <i>Journal of
 *              Trading</i> <b>1 (4)</b> 38-46
 *      </li>
 *      <li>
 *          Kissell, R., and R. Malamut (2007): Algorithmic Decision Making Framework <i>Journal of
 *              Trading</i> <b>1 (1)</b> 12-21
 *      </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/bayesian/README.md">Bayesian Price Based Optimal Execution</a></li>
 *  </ul>
 * 
 * @author Lakshmi Krishnamurthy
 */

public class PriorDriftDistribution extends org.drip.measure.gaussian.R1UnivariateNormal {

    /**
     * Construct an Instance of Prior Drift Distribution
     * 
     * @param dblExpectation Expectation of the Prior Drift
     * @param dblConfidence Confidence of the Prior Drift
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public PriorDriftDistribution (
        final double dblExpectation,
        final double dblConfidence)
        throws java.lang.Exception
    {
        super (dblExpectation, dblConfidence);
    }

    /**
     * Retrieve the Expectation of the Prior Drift Distribution
     * 
     * @return The Expectation of the Prior Drift Distribution
     */

    public double expectation()
    {
        return mean();
    }

    /**
     * Retrieve the Confidence of the Prior Drift Distribution
     * 
     * @return The Confidence of the Prior Drift Distribution
     */

    public double confidence()
    {
        return java.lang.Math.sqrt (variance());
    }

    /**
     * Generate the given Number of Bayesian Drift Realizations
     * 
     * @param iNumRealization The Number of Realizations to be generated
     * 
     * @return Array of the Drift Realizations
     */

    public double[] realizedDrift (
        final int iNumRealization)
    {
        if (0 >= iNumRealization) return null;

        double[] adblRealizedDrift = new double[iNumRealization];

        double dblConfidence = confidence();

        double dblExpectation = mean();

        for (int i = 0; i < iNumRealization; ++i) {
            try {
                adblRealizedDrift[i] = dblExpectation + dblConfidence *
                    org.drip.measure.gaussian.NormalQuadrature.InverseCDF (java.lang.Math.random());
            } catch (java.lang.Exception e) {
                e.printStackTrace();

                return null;
            }
        }

        return adblRealizedDrift;
    }
}