ruinprob.finite.sdp: Approximation of the probability of ruin within a finite time...

In finiteruinprob: Computation of the Probability of Ruin Within a Finite Time Horizon

Description

This function calculates an approximation to the probability of ruin within a finite time horizon for a compound Poisson risk process that is perturbed by a Wiener process. The approximation makes use of saddlepoint methods.

Usage

    ruinprob.finite.sdp(mgf, mgf.d1, mgf.d2, premium, freq, variance,
                        endpoint, verbose = FALSE)

Arguments

mgf	The moment-generating function of the individual claim amounts
mgf.d1	The first derivative of mgf
mgf.d2	The second derivative of mgf
premium	The premium force
freq	Frequency of the claims
variance	The variance of the Wiener process by which the risk process is perturbed
endpoint	The upper endpoint of mgf, i.e. the position of a pole
verbose	Return additional diagnostic information as an attribute of the output

Details

If neither or only the first derivative of mgf is provided, a numerical approximation to the missing derivative(s) will be used instead (see grad and hessian).

The argument endpoint is the (smallest) positive pole of mgf. Omitting this information will issue a warning and the value 1.0e+6 will be used instead, possibly yielding unexpected and unreliable output or leading to further errors.

Value

A function psi(x, t) taking as inputs the initial capital x and the time horizon t. This function returns a list, the first element of which contains a Lugannani–Rice-type approximation, the second one contains a Skovgaard-type approximation.

References

Gatto, R. and Baumgartner, B. (2016) Saddlepoint approximations to the probability of ruin in finite time for the compound Poisson risk process perturbed by diffusion. Methodology and Computing in Applied Probability 18(1), pp. 217-235.

finiteruinprob documentation built on May 2, 2019, 4:02 p.m.