Q.Stochastic.Process

Documentation

rwalkState :: RVarT (State Double) Double

type Time = Double

class Num b => Discretize d b where

Discretization of stochastic process over given interval

Methods

dDrift :: StochasticProcess a b => a -> d -> (Time, b) -> RVar b

Discretization of the drift process.

dDiff :: StochasticProcess a b => a -> d -> (Time, b) -> RVar b

Discretization of the diffusion process.

dDt :: StochasticProcess a b => a -> d -> (Time, b) -> Time

dt used.

Instances

(forall a b. StochasticProcess a Double) => Discretize EndEuler Double

Defined in Q.Stochastic.Discretize

Methods

dDrift :: StochasticProcess a Double => a -> EndEuler -> (Time, Double) -> RVar Double

dDiff :: StochasticProcess a Double => a -> EndEuler -> (Time, Double) -> RVar Double

dDt :: StochasticProcess a Double => a -> EndEuler -> (Time, Double) -> Time

Discretize Euler Double

Defined in Q.Stochastic.Discretize

Methods

dDrift :: StochasticProcess a Double => a -> Euler -> (Time, Double) -> RVar Double

dDiff :: StochasticProcess a Double => a -> Euler -> (Time, Double) -> RVar Double

dDt :: StochasticProcess a Double => a -> Euler -> (Time, Double) -> Time

Discretize Euler (Vector Double)

Defined in Q.Stochastic.Discretize

Methods

dDrift :: StochasticProcess a (Vector Double) => a -> Euler -> (Time, Vector Double) -> RVar (Vector Double)

dDiff :: StochasticProcess a (Vector Double) => a -> Euler -> (Time, Vector Double) -> RVar (Vector Double)

dDt :: StochasticProcess a (Vector Double) => a -> Euler -> (Time, Vector Double) -> Time

class Num b => StochasticProcess a b where

A stochastic process of the form \(dX_t = \mu(X_t, t)dt + \sigma(S_t, t)dB_t \)

Minimal complete definition

pDrift, pDiff

Methods

pDrift :: a -> (Time, b) -> RVar b

The process drift.

pDiff :: a -> (Time, b) -> RVar b

The process diffusion.

pEvolve

Arguments

:: Discretize d b

=> a

The process

-> d

Discretization scheme

-> (Time, b)

Initial state

-> Time

Target time t.

-> RVar b

\(dB_i\).

-> RVar b

\(X(t)\).

Evolve a process from a given state to a given time.

pEvolve' :: (Discretize d b, Num b) => a -> d -> (Time, b) -> RVar b -> RVar (Time, b)

Similar to evolve, but evolves the process with the discretization scheme \(dt\).

Instances

StochasticProcess GeometricBrownian Double

Defined in Q.Stochastic.Process

Methods

pDrift :: GeometricBrownian -> (Time, Double) -> RVar Double

pDiff :: GeometricBrownian -> (Time, Double) -> RVar Double

pEvolve :: Discretize d Double => GeometricBrownian -> d -> (Time, Double) -> Time -> RVar Double -> RVar Double

pEvolve' :: (Discretize d Double, Num Double) => GeometricBrownian -> d -> (Time, Double) -> RVar Double -> RVar (Time, Double)

data GeometricBrownian

Geometric Brownian motion

Constructors

GeometricBrownian

Fields

• gbDrift :: Double

  Drift

• gbDiff :: Double

  Vol

Instances

Show GeometricBrownian

Defined in Q.Stochastic.Process

Methods

showsPrec :: Int -> GeometricBrownian -> ShowS

show :: GeometricBrownian -> String

showList :: [GeometricBrownian] -> ShowS

StochasticProcess GeometricBrownian Double

Defined in Q.Stochastic.Process

Methods

pDrift :: GeometricBrownian -> (Time, Double) -> RVar Double

pDiff :: GeometricBrownian -> (Time, Double) -> RVar Double

pEvolve :: Discretize d Double => GeometricBrownian -> d -> (Time, Double) -> Time -> RVar Double -> RVar Double

pEvolve' :: (Discretize d Double, Num Double) => GeometricBrownian -> d -> (Time, Double) -> RVar Double -> RVar (Time, Double)

data ItoProcess

Ito process

Constructors

ItoProcess

Fields

• ipDrift :: (Time, Double) -> Double
• ipDiff :: (Time, Double) -> Double

Orphan instances

Num a => Num (RVarT m a)

Methods

(+) :: RVarT m a -> RVarT m a -> RVarT m a

(-) :: RVarT m a -> RVarT m a -> RVarT m a

(*) :: RVarT m a -> RVarT m a -> RVarT m a

negate :: RVarT m a -> RVarT m a

abs :: RVarT m a -> RVarT m a

signum :: RVarT m a -> RVarT m a

fromInteger :: Integer -> RVarT m a