org.drip.execution.risk

Class PowerVarianceObjectiveUtility

java.lang.Object

org.drip.execution.risk.PowerVarianceObjectiveUtility

All Implemented Interfaces:

ObjectiveUtility

public class PowerVarianceObjectiveUtility
extends java.lang.Object
implements ObjectiveUtility

PowerVarianceObjectiveUtility implements the Mean-Power-Variance Objective Utility Function that needs to be optimized to extract the Optimal Execution Trajectory. The Exact Objective Function is of the Form: U[x] = E[x] + lambda * (V[x] ^p) where p is greater than 0. p = 1 is the Regular Mean-Variance, and p = 0.5 is VaR Minimization (L-VaR). The References are: - Almgren, R., and N. Chriss (1999): Value under Liquidation, Risk 12 (12). - Almgren, R., and N. Chriss (2000): Optimal Execution of Portfolio Transactions, Journal of Risk, 3 (2), 5-39. - Almgren, R. (2003): Optimal Execution with Non-linear Impact Functions and Trading Enhanced Risk, Applied Mathematical Finance, 10, 1-18. - Artzner, P., F. Delbaen, J. M. Eber, and D. Heath (1999): Coherent Measures of Risk, Mathematical Finance, 9, 203-228. - Basak, S., and A. Shapiro (2001): Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices, Review of Financial Studies, 14, 371-405.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
PowerVarianceObjectiveUtility(double dblVarianceExponent, double dblRiskAversion) PowerVarianceObjectiveUtility Constructor

Method Summary

Modifier and Type	Method and Description
static PowerVarianceObjectiveUtility	LiquidityVaR(double dblRiskAversion) Generate the Liquidity VaR Version of the Power Variance Utility Function
double	riskAversion() Retrieve the Risk Aversion Parameter
ControlNodesGreek	sensitivity(TrajectoryControlNodesGreek tcngExpectation, TrajectoryControlNodesGreek tcngVariance) Generate the Objective Function Sensitivity given the Expectation and the Variance Control Node Sensitivity
double	varianceExponent() Retrieve the Variance Exponent

Methods inherited from class java.lang.Object

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

Constructor Detail

PowerVarianceObjectiveUtility

public PowerVarianceObjectiveUtility(double dblVarianceExponent,
                                     double dblRiskAversion)
                              throws java.lang.Exception

PowerVarianceObjectiveUtility Constructor

Parameters:

dblVarianceExponent - The Variance Exponent

dblRiskAversion - The Risk Aversion Parameter

Throws:

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

Method Detail

LiquidityVaR

public static final PowerVarianceObjectiveUtility LiquidityVaR(double dblRiskAversion)

Generate the Liquidity VaR Version of the Power Variance Utility Function

Parameters:

dblRiskAversion - The Risk Aversion Parameter

Returns:

The Liquidity VaR Version of the Power Variance Utility Function

riskAversion

public double riskAversion()

Retrieve the Risk Aversion Parameter

Returns:

The Risk Aversion Parameter

varianceExponent

public double varianceExponent()

Retrieve the Variance Exponent

Returns:

The Variance Exponent

sensitivity

public ControlNodesGreek sensitivity(TrajectoryControlNodesGreek tcngExpectation,
                                     TrajectoryControlNodesGreek tcngVariance)

Description copied from interface: ObjectiveUtility

Generate the Objective Function Sensitivity given the Expectation and the Variance Control Node Sensitivity

Specified by:

sensitivity in interface ObjectiveUtility

Parameters:

tcngExpectation - The Control Node Trajectory Expectation Sensitivity

tcngVariance - The Control Node Trajectory Variance Sensitivity

Returns:

The Control Node Trajectory Objective Function Sensitivity Sensitivity