# Value at Ruin

### Description

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

### Usage

1 2 3 | ```
varu(process, method = c("saddlepoint", "hypoexp"), ...)
hypoexpVaru(process)
saddlepointVaru(process, type = 2)
``` |

### Arguments

`process` |
a |

`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 |

### 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.

### 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.

### References

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

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