PriorConditionalCombiner.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>PriorConditionalCombiner</i> holds the Distributions associated with the Prior Drift and the
 * Conditional Price Distributions. It uses them to generate the resulting Joint, Posterior, and MAP Implied
 * Posterior Distributions. 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 PriorConditionalCombiner {
    private org.drip.execution.bayesian.PriorDriftDistribution _pdd = null;
    private org.drip.execution.bayesian.ConditionalPriceDistribution _cpd = null;

    /**
     * PriorConditionalCombiner Constructor
     * 
     * @param pdd The Prior Drift Distribution Instance
     * @param cpd The Conditional Price Distribution Instance
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public PriorConditionalCombiner (
        final org.drip.execution.bayesian.PriorDriftDistribution pdd,
        final org.drip.execution.bayesian.ConditionalPriceDistribution cpd)
        throws java.lang.Exception
    {
        if (null == (_pdd = pdd) || null == (_cpd = cpd))
            throw new java.lang.Exception ("PriorConditionalCombiner Constructor => Invalid Inputs");
    }

    /**
     * Retrieve the Prior Drift Distribution Instance
     * 
     * @return The Prior Drift Distribution Instance
     */

    public org.drip.execution.bayesian.PriorDriftDistribution prior()
    {
        return _pdd;
    }

    /**
     * Retrieve the Conditional Price Distribution Instance
     * 
     * @return The Conditional Price Distribution Instance
     */

    public org.drip.execution.bayesian.ConditionalPriceDistribution conditional()
    {
        return _cpd;
    }

    /**
     * Generate the Joint Price Distribution
     * 
     * @return The Joint Price Distribution
     */

    public org.drip.measure.gaussian.R1UnivariateNormal jointPriceDistribution()
    {
        double dblTime = _cpd.time();

        try {
            return new org.drip.measure.gaussian.R1UnivariateNormal (_pdd.expectation() * dblTime,
                _pdd.variance() * dblTime * dblTime +_cpd.variance());
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Generate the Posterior Drift Distribution
     * 
     * @param dblDeltaS The Price Change (Final - Initial)
     * 
     * @return The Posterior Drift Distribution
     */

    public org.drip.measure.gaussian.R1UnivariateNormal posteriorDriftDistribution (
        final double dblDeltaS)
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (dblDeltaS)) return null;

        double dblT = _cpd.time();

        double dblNuSquared = _pdd.variance();

        double dblSigmaSquared = _cpd.variance() / dblT;

        double dblPrecisionSquared = 1. / (dblSigmaSquared + dblNuSquared * dblT);

        try {
            return new org.drip.measure.gaussian.R1UnivariateNormal ((_pdd.expectation() * dblSigmaSquared +
                dblNuSquared * dblDeltaS) * dblPrecisionSquared, dblSigmaSquared * dblNuSquared *
                    dblPrecisionSquared);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }
}