# 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

 ```1 2``` ``` 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 30, 2017, 8:18 a.m.