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.
1 2 3
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
tvaru is a wrapper function for
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.
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