# tvaru: Tail Value at Ruin In sdprisk: Measures of Risk for the Compound Poisson Risk Process with Diffusion

## Description

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.

## Usage

 ```1 2 3``` ```tvaru(process, method = c("saddlepoint", "hypoexp"), ...) hypoexpTvaru(process) saddlepointTvaru(process, type = c("tail", "density"), ...) ```

## Arguments

 `process` a `"riskproc"` object. `method` character string indicating the calculation or approximation method. `type` 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`.

## Details

`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.

## Value

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`.

`varu`