Module net.finmath.lib
Package net.finmath.montecarlo

Class BrownianBridge

java.lang.Object
net.finmath.montecarlo.BrownianBridge
All Implemented Interfaces:
BrownianMotion, IndependentIncrements
public class BrownianBridge extends Object implements BrownianMotion
This class implements a Brownian bridge, i.e., samples of realizations of a Brownian motion conditional to a given start and end value.

A Brownian bridge is a conditional Brownian motion, i.e. for given random variables X and Y the Brownian bridge is
(W(t) | W(s) = X , W(T) = Y),
where W is a Brownian motion and s ≤ t ≤ T.

The samples of the Brownian bridge are generated by a Brownian motion which will be used to fill the gap between start and end. It is important that this Browninan motion is independent from the one which generated start and end, i.e. here: it should have a different seed.

The class implements the BrownianMotion, i.e., it only provides the increments of the Brownian bridge (however, in most application, like refinement of an Euler-scheme, this is exactly the desired object).

Note: The number of paths needs to be specified, because the start and the end point may be not stochastic, i.e. it is not possible to infer this quantity from the specified start and end.

Version:
1.0
Author:
Christian Fries
Date:
24.11.2013

  • Constructor Details

    • BrownianBridge

      public BrownianBridge(BrownianMotion generator, RandomVariable[] start, RandomVariable[] end)

    • BrownianBridge

      public BrownianBridge(TimeDiscretization timeDiscretization, int numberOfPaths, int seed, RandomVariable[] start, RandomVariable[] end)
      Construct a Brownian bridge, bridging from a given start to a given end.
      Parameters:
      timeDiscretization - The time discretization used for the Brownian increments.
      numberOfPaths - Number of paths to simulate.
      seed - The seed of the random number generator.
      start - Start value of the Brownian bridge.
      end - End value of the Brownian bridge.

    • BrownianBridge

      public BrownianBridge(TimeDiscretization timeDiscretization, int numberOfPaths, int seed, RandomVariable start, RandomVariable end)
      Construct a Brownian bridge, bridging from a given start to a given end.
      Parameters:
      timeDiscretization - The time discretization used for the Brownian increments.
      numberOfPaths - Number of paths to simulate.
      seed - The seed of the random number generator.
      start - Start value of the Brownian bridge.
      end - End value of the Brownian bridge.

  • Method Details

    • getBrownianIncrement

      public RandomVariable getBrownianIncrement(int timeIndex, int factor)
      Description copied from interface: BrownianMotion
      Return the Brownian increment for a given timeIndex. The method returns the random variable Δ Wj(ti) := Wj(ti+1)-W(ti) for the given time index i and a given factor (index) j
      Specified by:
      getBrownianIncrement in interface BrownianMotion
      Parameters:
      timeIndex - The time index (corresponding to the this class's time discretization).
      factor - The index of the factor (independent scalar Brownian increment).
      Returns:
      The factor (component) of the Brownian increments (a random variable).

    • getTimeDiscretization

      public TimeDiscretization getTimeDiscretization()
      Description copied from interface: BrownianMotion
      Returns the time discretization used for this set of time-discrete Brownian increments.
      Specified by:
      getTimeDiscretization in interface BrownianMotion
      Specified by:
      getTimeDiscretization in interface IndependentIncrements
      Returns:
      The time discretization used for this set of time-discrete Brownian increments.

    • getNumberOfFactors

      public int getNumberOfFactors()
      Description copied from interface: BrownianMotion
      Returns the number of factors.
      Specified by:
      getNumberOfFactors in interface BrownianMotion
      Specified by:
      getNumberOfFactors in interface IndependentIncrements
      Returns:
      The number of factors.

    • getNumberOfPaths

      public int getNumberOfPaths()
      Description copied from interface: BrownianMotion
      Returns the number of paths.
      Specified by:
      getNumberOfPaths in interface BrownianMotion
      Specified by:
      getNumberOfPaths in interface IndependentIncrements
      Returns:
      The number of paths.

    • getRandomVariableForConstant

      public RandomVariable getRandomVariableForConstant(double value)
      Description copied from interface: BrownianMotion
      Returns a random variable which is initialized to a constant, but has exactly the same number of paths or discretization points as the ones used by this BrownianMotion.
      Specified by:
      getRandomVariableForConstant in interface BrownianMotion
      Specified by:
      getRandomVariableForConstant in interface IndependentIncrements
      Parameters:
      value - The constant value to be used for initialized the random variable.
      Returns:
      A new random variable.

    • getCloneWithModifiedSeed

      public BrownianMotion getCloneWithModifiedSeed(int seed)
      Description copied from interface: BrownianMotion
      Return a new object implementing BrownianMotion having the same specifications as this object but a different seed for the random number generator. This method is useful if you like to make Monte-Carlo samplings by changing the seed.
      Specified by:
      getCloneWithModifiedSeed in interface BrownianMotion
      Specified by:
      getCloneWithModifiedSeed in interface IndependentIncrements
      Parameters:
      seed - New value for the seed.
      Returns:
      New object implementing BrownianMotion.

    • getCloneWithModifiedTimeDiscretization

      public BrownianMotion getCloneWithModifiedTimeDiscretization(TimeDiscretization newTimeDiscretization)
      Description copied from interface: BrownianMotion
      Return a new object implementing BrownianMotion having the same specifications as this object but a different time discretization.
      Specified by:
      getCloneWithModifiedTimeDiscretization in interface BrownianMotion
      Specified by:
      getCloneWithModifiedTimeDiscretization in interface IndependentIncrements
      Parameters:
      newTimeDiscretization - New time discretization
      Returns:
      New object implementing BrownianMotion.

    • getIncrement

      public RandomVariable[] getIncrement(int timeIndex)
      Description copied from interface: IndependentIncrements
      Return the increment for a given timeIndex. The method returns the random variable vector Δ X(ti) := X(ti+1)-X(ti) for the given time index i.
      Specified by:
      getIncrement in interface IndependentIncrements
      Parameters:
      timeIndex - The time index (corresponding to the this class's time discretization)
      Returns:
      The vector-valued increment (as a vector (array) of random variables).

    • getIncrement

      public RandomVariable getIncrement(int timeIndex, int factor)
      Description copied from interface: IndependentIncrements
      Return the increment for a given timeIndex and given factor. The method returns the random variable Δ Xj(ti) := Xj(ti+1)-X(ti) for the given time index i and a given factor (index) j
      Specified by:
      getIncrement in interface BrownianMotion
      Specified by:
      getIncrement in interface IndependentIncrements
      Parameters:
      timeIndex - The time index (corresponding to the this class's time discretization)
      factor - The index of the factor (independent scalar increment)
      Returns:
      The factor (component) of the increments (a random variable)

    • toString

      public String toString()
      Overrides:
      toString in class Object