Package org.drip.execution.hjb

Class NonDimensionalCostEvolver

java.lang.Object

org.drip.execution.hjb.NonDimensionalCostEvolver

Direct Known Subclasses:

NonDimensionalCostEvolverCorrelated, NonDimensionalCostEvolverSystemic

public abstract class NonDimensionalCostEvolver
extends java.lang.Object

NonDimensionalCostEvolver exposes the HJB-based Single Step Optimal Trajectory Cost Step Evolver using the Variants of the 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

Method Summary

Modifier and Type	Method	Description
boolean	asymptoticEnhancedEulerCorrection()	Retrieve the Asymptotic Enhanced Euler Correction Application Flag
double	asymptoticEulerUrgencyThreshold()	Retrieve the Asymptotic Euler Urgency Threshold
abstract NonDimensionalCost	evolve(NonDimensionalCost ndc, MarketState ms, double dblNonDimensionalRiskAversion, double dblNonDimensionalTime, double dblNonDimensionalTimeIncrement)	Evolve a Single Time Step of the Optimal Trajectory
OrnsteinUhlenbeck	ornsteinUnlenbeckProcess()	Retrieve the Reference Ornstein-Unlenbeck Process

Methods inherited from class java.lang.Object

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

Method Details

asymptoticEnhancedEulerCorrection

public boolean asymptoticEnhancedEulerCorrection()

Retrieve the Asymptotic Enhanced Euler Correction Application Flag

Returns:

The Asymptotic Enhanced Euler Correction Application Flag

asymptoticEulerUrgencyThreshold

public double asymptoticEulerUrgencyThreshold()

Retrieve the Asymptotic Euler Urgency Threshold

Returns:

The Asymptotic Euler Urgency Threshold

ornsteinUnlenbeckProcess

public OrnsteinUhlenbeck ornsteinUnlenbeckProcess()

Retrieve the Reference Ornstein-Unlenbeck Process

Returns:

The Reference Ornstein-Unlenbeck Process

evolve

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

Evolve a Single Time Step of the Optimal Trajectory

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