Package org.drip.execution.hjb

Class NonDimensionalCostEvolverSystemic

java.lang.Object

org.drip.execution.hjb.NonDimensionalCostEvolver

org.drip.execution.hjb.NonDimensionalCostEvolverSystemic

public class NonDimensionalCostEvolverSystemic
extends NonDimensionalCostEvolver

NonDimensionalCostEvolverSystemic implements the 1D HJB-based Single Step Optimal Trajectory Cost Step Evolver using the Systemic Coordinated Variation Version of the Stochastic Volatility and the Transaction Function arising from the Realization of the Market State Variable as described in the "Trading Time" Model. The References are:

• Almgren, R. F., and N. Chriss (2000): Optimal Execution of Portfolio Transactions Journal of Risk 3 (2) 5-39
• Almgren, R. F. (2009): Optimal Trading in a Dynamic Market https://www.math.nyu.edu/financial_mathematics/content/02_financial/2009-2.pdf
• Almgren, R. F. (2012): Optimal Trading with Stochastic Liquidity and Volatility SIAM Journal of Financial Mathematics 3 (1) 163-181
• Geman, H., D. B. Madan, and M. Yor (2001): Time Changes for Levy Processes Mathematical Finance 11 (1) 79-96
• Jones, C. M., G. Kaul, and M. L. Lipson (1994): Transactions, Volume, and Volatility Review of Financial Studies 7 (4) 631-651

• Module = Product Core Module
• Library = Transaction Cost Analytics
• Project = Optimal Impact/Capture Based Trading Trajectories - Deterministic, Stochastic, Static, and Dynamic
• Package = Hamilton Jacobin Bellman Based Optimal Evolution

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
NonDimensionalCostEvolverSystemic(OrnsteinUhlenbeck ou, double dblAsymptoticEulerUrgencyThreshold, boolean bAsymptoticEnhancedEulerCorrection)	NonDimensionalCostEvolverSystemic Constructor

Method Summary

Modifier and Type	Method	Description
NonDimensionalCost	evolve(NonDimensionalCost ndc, MarketState ms, double dblNonDimensionalRiskAversion, double dblNonDimensionalTime, double dblNonDimensionalTimeIncrement)	Evolve a Single Time Step of the Optimal Trajectory
static NonDimensionalCostEvolverSystemic	Standard(OrnsteinUhlenbeck ou)	Construct a Standard NonDimensionalCostEvolverSystemic Instance

Methods inherited from class org.drip.execution.hjb.NonDimensionalCostEvolver

asymptoticEnhancedEulerCorrection, asymptoticEulerUrgencyThreshold, ornsteinUnlenbeckProcess

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

NonDimensionalCostEvolverSystemic

public NonDimensionalCostEvolverSystemic(OrnsteinUhlenbeck ou,
double dblAsymptoticEulerUrgencyThreshold,
boolean bAsymptoticEnhancedEulerCorrection)
                                  throws java.lang.Exception

NonDimensionalCostEvolverSystemic Constructor

Parameters:

ou - The Underlying Ornstein-Unlenbeck Reference Process

bAsymptoticEnhancedEulerCorrection - Asymptotic Enhanced Euler Correction Application Flag

dblAsymptoticEulerUrgencyThreshold - The Asymptotic Euler Urgency Threshold

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

Standard

public static final NonDimensionalCostEvolverSystemic Standard(OrnsteinUhlenbeck ou)

Construct a Standard NonDimensionalCostEvolverSystemic Instance

Parameters:

ou - The Underlying Ornstein-Unlenbeck Reference Process

Returns:

The Standard NonDimensionalCostEvolverSystemic Instance

evolve

public NonDimensionalCost evolve(NonDimensionalCost ndc,
MarketState ms,
double dblNonDimensionalRiskAversion,
double dblNonDimensionalTime,
double dblNonDimensionalTimeIncrement)

Description copied from class: NonDimensionalCostEvolver

Evolve a Single Time Step of the Optimal Trajectory

Specified by:

evolve in class NonDimensionalCostEvolver

Parameters:

ndc - The Initial Non Dimensional Cost Value Function

ms - The Market State

dblNonDimensionalRiskAversion - The Non Dimensional Risk Aversion Parameter

dblNonDimensionalTime - The Non Dimensional Time Node

dblNonDimensionalTimeIncrement - The Non Dimensional Time Increment

Returns:

The Post Evolved Non-dimensional Cost Value Function