Simulation of a risk process that is perturbed by a Wiener process

Description

This function simulates paths of a compound Poisson risk process that is perturbed by a Wiener process. Multiple paths can be simulated simultaneously.

Usage

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rriskproc(m = 1001, window = c(0, 1), num = 1,
          sigma = 1, freq = 1, drift = 0, jumpdist, ...)

Arguments

m

Number of sample points for each path

window

Beginning and end of the time window

num

Number of paths to be simulated

sigma

Volatility of the Wiener process

freq

Frequency of the claims

drift

Drift (premium intensity) of the process

jumpdist

A function that returns realizations of the claim distribution

...

Additional arguments for jumpdist

Details

Possible choices for jumpdist include rexp, rgamma and rlnorm.

It is assumed that the function specified for jumpdist interprets its first argument as the vector length of its return value, i. e. the number of simultaneously generated random variables.

The path realizations of the Wiener process are generated using the circulant embedding method (see references).

Value

A time-series object/time-series object containing the simulated sample path(s).

References

Dietrich, C. and Newsam, G. (1997) Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix. SIAM Journal on Scientific Computing 18(4), pp. 1088-1107

See Also

rhypoexp

Examples

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    require(sdprisk)

    rriskproc(m        = 1001,
              window   = c(0, 5),
              num      = 1,
              sigma    = sqrt(0.4),
              freq     = 1,
              drift    = 2,
              jumpdist = rhypoexp,
              rate     = c(1, 10))

    # The same can be achieved using
    #   jumpdist = function(n) rexp(n, 1) + rexp(n, 10)

    rriskproc(window = c(0, 10),
              jumpdist = function(n) {
                  rexp(n, 1) + rexp(n, 10)
              })