yuima (version 1.1.6)

setFunctional: Description of a functional associated with a perturbed stochastic differential equation

Description

This function is used to give a description of the stochastic differential equation. The functional represent the price of the option in financial economics, for example.

Usage

setFunctional(model, F, f, xinit,e)

Arguments

model

yuima or yuima.model object.

F

function of $X_t$ and $epsilon$

f

list of functions of $X_t$ and $epsilon$

xinit

initial values of state variable.

e

epsilon parameter

Value

Details

You should look at the vignette and examples.

The object foi contains several ``slots''. To see inside its structure we use the R command str. f and Fare R (list of) expressions which contains the functional of interest specification. e is a small parameter on which we conduct asymptotic expansion of the functional.

Examples

set.seed(123)
# to the Black-Scholes economy:
# dXt^e = Xt^e * dt + e * Xt^e * dWt
diff.matrix <- matrix( c("x*e"), 1,1)
model <- setModel(drift = c("x"), diffusion = diff.matrix)
# call option is evaluated by averating
# max{ (1/T)*int_0^T Xt^e dt, 0}, the first argument is the functional of interest:
Terminal <- 1
xinit <- c(1)
f <- list( c(expression(x/Terminal)), c(expression(0)))
F <- 0
division <- 1000
e <- .3
yuima <- setYuima(model = model,sampling = setSampling(Terminal = Terminal, n = division))
yuima <- setFunctional( model = yuima, xinit=xinit, f=f,F=F,e=e)
# look at the model structure
str(yuima@functional)