SingleRandomSequenceBound.java

package org.drip.sample.sequence;

import org.drip.function.definition.R1ToR1;
import org.drip.function.r1tor1.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.sequence.metrics.*;
import org.drip.sequence.random.BoundedUniform;
import org.drip.service.env.EnvManager;

/*

 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * Copyright (C) 2015 Lakshmi Krishnamurthy
 * 
 *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
 *      libraries targeting analysts and developers
 *      https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *      Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  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.
 */

/**
 * SingleRandomSequenceBound demonstrates the Computation of the Probabilistic Bounds for a Sample Random
 *  Sequence.
 *
 * @author Lakshmi Krishnamurthy
 */

public class SingleRandomSequenceBound {

    private static final void MarkovBound (
        final SingleSequenceAgnosticMetrics sm,
        final double dblLevel,
        final R1ToR1 au)
        throws Exception
    {
        System.out.println (
            (null == au ? "\tMarkov Base Bound        [" :  "\tMarkov Function Bound    [") +
            FormatUtil.FormatDouble (dblLevel, 1, 2, 1.) + "] : " +
            FormatUtil.FormatDouble (sm.markovUpperProbabilityBound (dblLevel, au), 1, 4, 1.) + " |" +
            FormatUtil.FormatDouble (1. - dblLevel, 1, 4, 1.)
        );
    }

    private static final void ChebyshevBound (
        final SingleSequenceAgnosticMetrics sm,
        final double dblLevel)
        throws Exception
    {
        System.out.println (
            "\tChebyshev Bound          [" +
            FormatUtil.FormatDouble (dblLevel, 1, 2, 1.) + "] : " +
            FormatUtil.FormatDouble (sm.chebyshevBound (dblLevel).lower(), 1, 4, 1.) + " |" +
            FormatUtil.FormatDouble (sm.chebyshevBound (dblLevel).upper(), 1, 4, 1.) + " |" +
            FormatUtil.FormatDouble (1. - 2. * dblLevel, 1, 4, 1.)
        );
    }

    private static final void ChebyshevCantelliBound (
        final SingleSequenceAgnosticMetrics sm,
        final double dblLevel)
        throws Exception
    {
        System.out.println (
            "\tChebyshev Cantelli Bound [" +
            FormatUtil.FormatDouble (dblLevel, 1, 2, 1.) + "] : " +
            "        |" +
            FormatUtil.FormatDouble (sm.chebyshevCantelliBound (dblLevel).upper(), 1, 4, 1.) + " |" +
            FormatUtil.FormatDouble (1. - dblLevel, 1, 4, 1.)
        );
    }

    private static final void CentralMomentBound (
        final SingleSequenceAgnosticMetrics sm,
        final double dblLevel,
        final int iMoment)
        throws Exception
    {
        System.out.println (
            "\tMoment #" + iMoment + " Bound          [" +
            FormatUtil.FormatDouble (dblLevel, 1, 2, 1.) + "] : " +
            FormatUtil.FormatDouble (sm.centralMomentBound (dblLevel, iMoment).lower(), 1, 4, 1.) + " |" +
            FormatUtil.FormatDouble (sm.centralMomentBound (dblLevel, iMoment).upper(), 1, 4, 1.) + " |" +
            FormatUtil.FormatDouble (1. - 2. * dblLevel, 1, 4, 1.)
        );
    }

    private static final void MarkovBound (
        final SingleSequenceAgnosticMetrics sm,
        final R1ToR1 au)
        throws Exception
    {
        MarkovBound (sm, 0.20, au);

        MarkovBound (sm, 0.40, au);

        MarkovBound (sm, 0.59, au);

        MarkovBound (sm, 0.79, au);

        MarkovBound (sm, 0.99, au);
    }

    private static final void ChebyshevBound (
        final SingleSequenceAgnosticMetrics sm)
        throws Exception
    {
        ChebyshevBound (sm, 0.20);

        ChebyshevBound (sm, 0.25);

        ChebyshevBound (sm, 0.30);

        ChebyshevBound (sm, 0.35);

        ChebyshevBound (sm, 0.40);
    }

    private static final void ChebyshevCantelliBound (
        final SingleSequenceAgnosticMetrics sm)
        throws Exception
    {
        ChebyshevCantelliBound (sm, 0.20);

        ChebyshevCantelliBound (sm, 0.25);

        ChebyshevCantelliBound (sm, 0.30);

        ChebyshevCantelliBound (sm, 0.35);

        ChebyshevCantelliBound (sm, 0.40);
    }

    private static final void CentralMomentBound (
        final SingleSequenceAgnosticMetrics sm,
        final int iMoment)
        throws Exception
    {
        CentralMomentBound (sm, 0.20, iMoment);

        CentralMomentBound (sm, 0.25, iMoment);

        CentralMomentBound (sm, 0.30, iMoment);

        CentralMomentBound (sm, 0.35, iMoment);

        CentralMomentBound (sm, 0.40, iMoment);
    }

    private static final void SequenceGenerationRun (
        final SingleSequenceAgnosticMetrics sm)
        throws Exception
    {
        System.out.println ("\tExpectation                      : " + FormatUtil.FormatDouble (sm.empiricalExpectation(), 1, 4, 1.));

        System.out.println ("\tVariance                         : " + FormatUtil.FormatDouble (sm.empiricalVariance(), 1, 4, 1.));

        System.out.println ("\t---------------------------------------------------");

        MarkovBound (sm, new ExponentialTension (Math.E, 0.1));

        System.out.println ("\t---------------------------------------------------");

        MarkovBound (sm, new ExponentialTension (Math.E, 1.0));

        System.out.println ("\t---------------------------------------------------");

        MarkovBound (sm, new ExponentialTension (Math.E, 5.0));

        System.out.println ("\t---------------------------------------------------");

        MarkovBound (sm, null);

        System.out.println ("\t---------------------------------------------------");

        ChebyshevBound (sm);

        System.out.println ("\t---------------------------------------------------");

        ChebyshevCantelliBound (sm);

        System.out.println ("\t---------------------------------------------------");

        CentralMomentBound (sm, 3);

        System.out.println ("\t---------------------------------------------------");

        CentralMomentBound (sm, 4);

        System.out.println ("\t---------------------------------------------------");

        CentralMomentBound (sm, 5);
    }

    public static void main (
        final String[] astrArgs)
        throws Exception
    {
        EnvManager.InitEnv ("");

        /* System.out.println ("\t---------------------------------------------------");

        System.out.println ("\t|              BOUNDED GAUSSIAN RUN               |");

        System.out.println ("\t---------------------------------------------------");

        SequenceGenerationRun (new BoundedGaussian (0.5, 1., 0., 1.).sequence (50000, null));

        System.out.println ("\t---------------------------------------------------");

        System.out.println(); */

        System.out.println ("\t---------------------------------------------------");

        System.out.println ("\t|              BOUNDED UNIFORM RUN                |");

        System.out.println ("\t---------------------------------------------------");

        SequenceGenerationRun (new BoundedUniform (0., 1.).sequence (50000, null));

        System.out.println ("\t---------------------------------------------------");
    }
}