Tail Value at Ruin


The tail value at ruin for a given probability level ε is defined as the conditional expectation of the maximal aggregate loss given that it is above the value at ruin of level ε.


tvaru(process, method = c("saddlepoint", "hypoexp"), ...)
saddlepointTvaru(process, type = c("tail", "density"), ...)



a "riskproc" object.


character string indicating the calculation or approximation method.


character string indicating which function is to be used for the approximation.


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


tvaru is a wrapper function for hypoexpTvaru and saddlepointTvaru.

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

saddlepointTvaru uses saddlepoint techniques for the approximation of the tail value at ruin. More precisely, the saddlepoint approximation to the probability of is numerically integrated in the frequency domain, and implicitly also the saddlepoint approximation to the value at ruin (see varu) is used. If type = "tail" the integrand is the probability of ruin (as function in the frequency domain), otherwise (type = "density") it is essentially a re-scaled version of the probability of ruin due to claims. The former requires fewer calculations and seems to produce slightly more accurate results.


A function returning the tail value at ruin of a given probability level is returned.

If method = "saddlepoint" or if saddlepointTvaru is used, the returned function has an additional second argument giving the number of iterations used for the approximation of the value at ruin (i. e., the lower integration limit), see varu.

See Also


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