SC19038: R Package of SC19038

Description Usage Arguments Details Value Author(s) References Examples

View source: R/simuGBM.R

Simulation and plotting of:
1. k-dim (k ≥ 1; k ≤ 3 for plotting) general Brownian motion (i.e. Brownian motion with drift) or its running maximum process (when k = 1);
2. 1-dim geometric Brownian motion.

simuGBM(
  x_init = 0.1,
  t_init = 0,
  t_end = 1,
  lag = 0.001,
  dim = 1,
  mu = numeric(dim),
  sigma = replicate(dim, 1),
  run_max = FALSE,
  type = c("General", "Geometric"),
  plot = TRUE,
  seed = 19038,
  ...
)

`x_init`	The k-dim initial value of the process to be generated. 1. k ≥ 1 for `type = "General"`; 2. k = 1 for `type = "Geometric"`; 3. k ≤ 3 for `plot = TRUE`.
`t_init`	The initial time of the process to be generated.
`t_end`	The end time of the process to be generated.
`lag`	The consistent time lag of every two contiguous points to be generated.
`dim`	The dimension of the process to be generated.
`mu`	See details.
`sigma`	See details.
`run_max`	`TRUE/FALSE(default)`. If `run_max = TRUE`, then the running maximum process will be generated.
`type`	`"General"/"Geometric"`.
`plot`	`TRUE(default)/FALSE`. If `plot = FALSE`, the `fig` item will be returned as `NULL`.
`seed`	The random seed. The default value is 19038.
`...`	The parameters passed to `plot` or `scatterplot3d`.

General Brownian motion: U_t = x₀ + μ·t + σ·B_t;
Running maximum process: M_t = max_t∈T{B_t};
Geometric Brownian motion: V_t = x₀·exp{(μ - σ²/2)·t + σ·B_t}.

A list containing:

`val`	The values of the generated process.
`fig`	The plot of the generated process (`plot = TRUE`) or `NULL` (`plot = FALSE`).

Dong-Liang Wang

Pacati, C. (2010-11). Brownian Motion and Geometric Brownian Motion.
http://www-users.math.umn.edu/~grayx004/pdf/FM5002/BMandGBMdoc.pdf.

res <- simuGBM(x_init = c(1, 0, 1), lag = 1e-4, dim = 3, 
               type = "General", plot = TRUE, seed = 1,
               xlab = bquote(X[1]), ylab = bquote(X[2]), zlab = bquote(X[3]))
print(res$val)