varu: Value at Ruin

Description

The value at ruin at a given probability level $\varepsilon$ is defined as the minimal capital that is required in order to have a ruin probability of at most $\varepsilon$. This is equivalent to the $(1-\varepsilon)$-quantile of the maximal aggregate loss.

Usage

varu(process, method = c("saddlepoint", "hypoexp"), ...)
hypoexpVaru(process)
saddlepointVaru(process, type = 2)

Arguments

process

a "riskproc" object.

method

character string indicating the calculation or approximation method.

type

number indicating the type of approximation; possible choices are 1 and 2.

...

further arguments that are passed on to saddlepointVaru, depending on the value of method.

Value

A function returning the value at ruin of a given probability level is returned.
If method = "saddlepoint" or if saddlepointVaru is used, the returned function has an additional second argument giving the number of iterations.

Details

varu is a wrapper function for hypoexpVaru and saddlepointVaru.

hypoexpVaru calculates the value at ruin in the case of hypo-exponentially distributed claim amounts by numerical inversion of the probability of ruin, which can be computed exactly.

saddlepointVaru uses saddlepoint techniques for the approximation of the value at ruin, more specifically, the inversion algorithms provided by Wang (1995). The first one (type = 1) is only given for completeness (or comparison purposes), because, due to repeatedly switching back and forth between the monetary domain the frequency (saddlepoint) domain, it is much slower than the second one (type = 2), which is performed entirely in the frequency domain. Refer to the references given below for more details.

References

Wang, Suojin (1995) One-Step Saddlepoint Approximations for Quantiles. Computational Statistics and Data Analysis 20(1), pp. 65--74.