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1-dimensional stochastic process

This class describes a stochastic process governed by $$ dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. $$

Hierarchy

Implements

Index

Properties

_discretization

_discretization: discretization

_isDisposed

_isDisposed: boolean = false

_observables

_observables: Set<Observable> = new Set()

_observers

_observers: Set<Observer> = new Set()

dispose

dispose: () => void

Type declaration

    • (): void
    • Returns void

isDisposed

isDisposed: boolean

notifyObservers

notifyObservers: () => void

Type declaration

    • (): void
    • Returns void

registerObserver

registerObserver: (o: Observer) => void

Type declaration

registerWith

registerWith: (h: Observable) => void

Type declaration

registerWithObservables

registerWithObservables: (o: Observer) => void

Type declaration

unregisterObserver

unregisterObserver: (o: Observer) => void

Type declaration

unregisterWith

unregisterWith: (h: Observable) => Size

Type declaration

unregisterWithAll

unregisterWithAll: () => void

Type declaration

    • (): void
    • Returns void

Methods

apply1

apply2

  • applies a change to the asset value. By default, it returns $ x + \Delta x $.

    Parameters

    Returns Real

covariance

deepUpdate

  • deepUpdate(): void

diffusion1

diffusion2

  • brief returns the diffusion part of the equation, i.e. $ \sigma(t, x_t) $

    Parameters

    Returns Real

drift1

drift2

  • returns the drift part of the equation, i.e. $ \mu(t, x_t) $

    Parameters

    Returns Real

evolve1

evolve2

  • returns the asset value after a time interval $ \Delta t $ according to the given discretization. By default, it returns $$ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w $$ where $ E $ is the expectation and $ S $ the standard deviation.

    Parameters

    Returns Real

expectation1

expectation2

  • returns the expectation $$ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

    Parameters

    Returns Real

factors

  • returns the number of independent factors of the process

    Returns Size

init

initialValues

  • initialValues(): Real[]

size

stdDeviation1

stdDeviation2

  • returns the standard deviation $$ S(x_{t_0 + \Delta t} | x_{t_0} = x_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

    Parameters

    Returns Real

time

  • time(d: Date): Time
  • returns the time value corresponding to the given date in the reference system of the stochastic process.

    note As a number of processes might not need this functionality, a default implementation is given which raises an exception.

    Parameters

    • d: Date

    Returns Time

update

  • update(): void

variance

  • returns the variance $$ V(x_{t_0 + \Delta t} | x_{t_0} = x_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

    Parameters

    Returns Real

x0

  • returns the initial value of the state variable

    Returns Real