R1StochasticEvolver.java
package org.drip.dynamics.process;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 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>R1StochasticEvolver</i> implements the R<sup>1</sup> Stochastic Evolver. The References are:
*
* <br><br>
* <ul>
* <li>
* Doob, J. L. (1942): The Brownian Movement and Stochastic Equations <i>Annals of Mathematics</i>
* <b>43 (2)</b> 351-369
* </li>
* <li>
* Gardiner, C. W. (2009): <i>Stochastic Methods: A Handbook for the Natural and Social Sciences
* 4<sup>th</sup> Edition</i> <b>Springer-Verlag</b>
* </li>
* <li>
* Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
* <b>World Scientific</b>
* </li>
* <li>
* Karatzas, I., and S. E. Shreve (1991): <i>Brownian Motion and Stochastic Calculus 2<sup>nd</sup>
* Edition</i> <b>Springer-Verlag</b>
* </li>
* <li>
* Risken, H., and F. Till (1996): <i>The Fokker-Planck Equation – Methods of Solution and
* Applications</i> <b>Springer</b>
* </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/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/README.md">HJM, Hull White, LMM, and SABR Dynamic Evolution Models</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/process/README.md">Ito-Dynamics Based Stochastic Process</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1StochasticEvolver
{
private org.drip.dynamics.ito.R1ToR1Drift _driftFunction = null;
private org.drip.dynamics.ito.R1ToR1Volatility _volatilityFunction = null;
private org.drip.dynamics.ito.R1StochasticDriver _stochasticDriver = null;
/**
* R1StochasticEvolver Constructor
*
* @param driftFunction Drift Function
* @param volatilityFunction Volatility Function
* @param stochasticDriver Stochastic Driver
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public R1StochasticEvolver (
final org.drip.dynamics.ito.R1ToR1Drift driftFunction,
final org.drip.dynamics.ito.R1ToR1Volatility volatilityFunction,
final org.drip.dynamics.ito.R1StochasticDriver stochasticDriver)
throws java.lang.Exception
{
if (null == (_driftFunction = driftFunction) ||
null == (_volatilityFunction = volatilityFunction) ||
null == (_stochasticDriver = stochasticDriver))
{
throw new java.lang.Exception (
"R1StochasticEvolver Constructor => Invalid Inputs"
);
}
}
/**
* Retrieve the Drift Function
*
* @return The Drift Function
*/
public org.drip.dynamics.ito.R1ToR1Drift driftFunction()
{
return _driftFunction;
}
/**
* Retrieve the Volatility Function
*
* @return The Volatility Function
*/
public org.drip.dynamics.ito.R1ToR1Volatility volatilityFunction()
{
return _volatilityFunction;
}
/**
* Retrieve the Stochastic Driver
*
* @return The Stochastic Driver
*/
public org.drip.dynamics.ito.R1StochasticDriver stochasticDriver()
{
return _stochasticDriver;
}
/**
* Generate the Next Vertex in the Iteration
*
* @param currentVertex The Current Vertex
* @param timeIncrement The Time Increment
*
* @return The Next Vertex
*/
public org.drip.dynamics.ito.TimeR1Vertex evolve (
final org.drip.dynamics.ito.TimeR1Vertex currentVertex,
final double timeIncrement)
{
if (null == currentVertex ||
!org.drip.numerical.common.NumberUtil.IsValid (
timeIncrement
)
)
{
return null;
}
try
{
return new org.drip.dynamics.ito.TimeR1Vertex (
currentVertex.t() + timeIncrement,
currentVertex.x() + _driftFunction.drift (
currentVertex
) * timeIncrement + _volatilityFunction.volatility (
currentVertex
) * _stochasticDriver.emitSingle()
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Estimate the Temporal Central Measures for the Underlier given the Delta 0 Starting PDF
*
* @param x0 The X Anchor for the Delta Function
* @param t The Forward Time
*
* @return The Temporal Central Measures for the Underlier
*/
public org.drip.measure.statistics.PopulationCentralMeasures temporalPopulationCentralMeasures (
final double x0,
final double t)
{
return null;
}
/**
* Generate the Steady State Population Central Measures
*
* @param x0 Starting Variate
*
* @return The Steady State Population Central Measures
*/
public org.drip.measure.statistics.PopulationCentralMeasures steadyStatePopulationCentralMeasures (
final double x0)
{
return null;
}
/**
* Construct the Fokker Planck PDF Generator corresponding to R<sup>1</sup> Stochastic Evolver
*
* @return The Fokker Planck PDF Generator corresponding to R<sup>1</sup> Stochastic Evolver
*/
public org.drip.dynamics.kolmogorov.R1FokkerPlanck fokkerPlanckGenerator()
{
try
{
new org.drip.dynamics.kolmogorov.R1FokkerPlanck (
_driftFunction,
_volatilityFunction
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Generate the Future Value Distribution at Time t
*
* @param x0 Starting Variate
* @param t Time
*
* @return The Future Value Distribution
*/
public org.drip.measure.continuous.R1Univariate futureValueDistribution (
final double x0,
final double t)
{
return null;
}
}