RdStochasticEvolver.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>RdStochasticEvolver</i> implements the R<sup>d</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 RdStochasticEvolver
{
private org.drip.dynamics.ito.RdToR1Drift[] _driftFunctionArray = null;
private org.drip.dynamics.ito.RdStochasticDriver _stochasticDriver = null;
private org.drip.dynamics.ito.RdToR1Volatility[][] _volatilityFunctionGrid = null;
private double[] pointDriftArray (
final org.drip.dynamics.ito.TimeRdVertex currentVertex)
{
int dimension = _driftFunctionArray.length;
double[] pointDriftArray = new double[dimension];
for (int dimensionIndex = 0;
dimensionIndex < dimension;
++dimensionIndex)
{
try
{
pointDriftArray[dimensionIndex] = _driftFunctionArray[dimensionIndex].drift (
currentVertex
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
return pointDriftArray;
}
private double[][] pointVolatilityGrid (
final org.drip.dynamics.ito.TimeRdVertex currentVertex)
{
int dimension = _volatilityFunctionGrid.length;
double[][] pointVolatilityGrid = new double[dimension][dimension];
for (int dimensionIndexI = 0;
dimensionIndexI < dimension;
++dimensionIndexI)
{
for (int dimensionIndexJ = 0;
dimensionIndexJ < dimension;
++dimensionIndexJ)
{
try
{
pointVolatilityGrid[dimensionIndexI][dimensionIndexJ] =
_volatilityFunctionGrid[dimensionIndexI][dimensionIndexJ].volatility (
currentVertex
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
}
return pointVolatilityGrid;
}
/**
* RdStochasticEvolver Constructor
*
* @param driftFunctionArray The Drift Function Array
* @param volatilityFunctionGrid The Volatility Function Grid
* @param stochasticDriver The Stochastic Driver
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public RdStochasticEvolver (
final org.drip.dynamics.ito.RdToR1Drift[] driftFunctionArray,
final org.drip.dynamics.ito.RdToR1Volatility[][] volatilityFunctionGrid,
final org.drip.dynamics.ito.RdStochasticDriver stochasticDriver)
throws java.lang.Exception
{
if (null == (_driftFunctionArray = driftFunctionArray) ||
null == (_volatilityFunctionGrid = volatilityFunctionGrid) ||
null == (_stochasticDriver = stochasticDriver))
{
throw new java.lang.Exception (
"RdStochasticEvolver Constructor => Invalid Inputs"
);
}
int dimension = _driftFunctionArray.length;
if (0 == dimension ||
dimension != _volatilityFunctionGrid.length ||
null == _volatilityFunctionGrid[0] ||
dimension != _volatilityFunctionGrid[0].length)
{
throw new java.lang.Exception (
"RdStochasticEvolver Constructor => Invalid Inputs"
);
}
for (int dimensionIndexI = 0;
dimensionIndexI < dimension;
++dimensionIndexI)
{
if (null == _driftFunctionArray[dimensionIndexI])
{
throw new java.lang.Exception (
"RdStochasticEvolver Constructor => Invalid Inputs"
);
}
for (int dimensionIndexJ = 0;
dimensionIndexJ < dimension;
++dimensionIndexJ)
{
if (null == _volatilityFunctionGrid[dimensionIndexI][dimensionIndexJ])
{
throw new java.lang.Exception (
"RdStochasticEvolver Constructor => Invalid Inputs"
);
}
}
}
}
/**
* Retrieve the Drift Function Array
*
* @return The Drift Function Array
*/
public org.drip.dynamics.ito.RdToR1Drift[] driftFunctionArray()
{
return _driftFunctionArray;
}
/**
* Retrieve the Volatility Function Grid
*
* @return The Volatility Function Grid
*/
public org.drip.dynamics.ito.RdToR1Volatility[][] volatilityFunctionGrid()
{
return _volatilityFunctionGrid;
}
/**
* Retrieve the Stochastic Driver
*
* @return The Stochastic Driver
*/
public org.drip.dynamics.ito.RdStochasticDriver 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.TimeRdVertex evolve (
final org.drip.dynamics.ito.TimeRdVertex currentVertex,
final double timeIncrement)
{
if (null == currentVertex ||
!org.drip.numerical.common.NumberUtil.IsValid (
timeIncrement
)
)
{
return null;
}
double[] pointDriftArray = pointDriftArray (
currentVertex
);
if (null == pointDriftArray)
{
return null;
}
double[] volatilityShiftArray = org.drip.numerical.linearalgebra.Matrix.Product (
pointVolatilityGrid (
currentVertex
),
_stochasticDriver.emitSingle()
);
if (null == volatilityShiftArray)
{
return null;
}
int dimension = _driftFunctionArray.length;
double[] xNextArray = new double[dimension];
double[] xCurrentArray = currentVertex.xArray();
for (int dimensionIndex = 0;
dimensionIndex < dimension;
++dimensionIndex)
{
xNextArray[dimensionIndex] = xCurrentArray[dimensionIndex] +
pointDriftArray[dimensionIndex] * timeIncrement +
volatilityShiftArray[dimensionIndex];
}
try
{
return new org.drip.dynamics.ito.TimeRdVertex (
currentVertex.t() + timeIncrement,
xNextArray
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Construct the Fokker Planck PDF Generator corresponding to R<sup>d</sup> Stochastic Evolver
*
* @return The Fokker Planck PDF Generator corresponding to R<sup>d</sup> Stochastic Evolver
*/
public org.drip.dynamics.kolmogorov.RdFokkerPlanck fokkerPlanckGenerator()
{
try
{
return new org.drip.dynamics.kolmogorov.RdFokkerPlanck (
_driftFunctionArray,
new org.drip.dynamics.ito.DiffusionTensor (
_volatilityFunctionGrid
),
null
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
}