ruinprob.finite.sdp {finiteruinprob} | R Documentation |
Approximation of the probability of ruin within a finite time horizon using saddlepoint methods
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.d2 |
The second derivative of |
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 |
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.