Simulations Functions

In this section we document data structures and methods for Monte Carlo simulation and path setup.

Monte Carlo Simulation

DiffFusion.Simulation — Type
struct Simulation
    model::Model
    times::AbstractVector
    X::AbstractArray
end

A Simulation object represents the result of a Monte Carlo simulation.

Elements are:

  • model - the model used for simulation.
  • times - vector of simulation times starting with 0.
  • X - tensor of size (N_1, N_2, N_3) and type ModelValue where
    • N_1 is length(m.state_alias),
    • N_2 is number of Monte Carlo paths,
    • N_3 is length(times).
DiffFusion.pseudo_brownian_increments — Function
pseudo_brownian_increments(
    n_states::Int,
    n_paths::Int,
    n_times::Int,  # without zero
    seed::Int = 271828182846,
    )

A simple method to generate Brownian motion increments.

DiffFusion.sobol_brownian_increments — Function
sobol_brownian_increments(
    n_states::Int,
    n_paths::Int,
    n_times::Int,  # without zero
    )

Generate Brownian motion increments via Sobol sequence.

DiffFusion.simple_simulation — Function
simple_simulation(
    model::Model,
    ch::CorrelationHolder,
    times::AbstractVector,
    n_paths::Int;
    with_progress_bar::Bool = true,
    brownian_increments::Function = pseudo_brownian_increments
    )

A simple Monte Carlo simulation method assuming all model components are state-independent.