aeExpectation function

Asymptotic Expansion - Functionals

Compute the expected value of functionals.

aeExpectation(f, bounds, ae, eps = 1, order = NULL, ...)

Arguments

• f: character. The functional.
• bounds: named list of integration bounds in the form list(x = c(xmin, xmax), y = c(ymin, ymax), ...)
• ae: an object of class yuima.ae-class.
• eps: numeric. The intensity of the perturbation.
• order: integer. The expansion order. If NULL (default), it uses the maximum order used in ae.
• ...: additional arguments passed to cubintegrate.

Returns

return value of cubintegrate. The expectation of the functional provided.

Examples

## Not run:

# model
gbm <- setModel(drift = 'mu*x', diffusion = 'sigma*x', solve.variable = 'x')

# settings
xinit <- 100
par <- list(mu = 0.01, sigma = 0.2)
sampling <- setSampling(Initial = 0, Terminal = 1, n = 1000)

# asymptotic expansion
approx <- ae(model = gbm, sampling = sampling, order = 4, true.parameter = par, xinit = xinit)

# compute the mean via integration
aeExpectation(f = 'x', bounds = list(x = c(0,1000)), ae = approx)

# compare with the mean computed by differentiation of the characteristic function
aeMean(approx)
## End(Not run)