Computes the lower quantile VaR at level p: the smallest x for which F_X(x) >= p. No interpolation across probability atoms; for discrete claims, the quantile is an observed support point, not an interpolated monetary amount.
Arguments
- x
A vector of observed losses, a tibble of simulations, a severity specification with an exact quantile, or an [aggregate_distribution()] result. A zero-payment specification is also accepted.
- level
Probability levels strictly between zero and one.
- value
Optional character name of a loss column in a data frame. By default, `aggregate_loss`, `claim_amount`, `claim_count`, `loss`, or `payment` is selected (in that order).
Details
The tail probability retained by an aggregate-distribution object is never renormalized away. Quantiles in its uncomputed tail are rejected. For sampled losses the definition is empirical, not a model-based claim. FFT count truncation can omit probability at small losses as well as large losses. If the omitted count mass could move the selected quantile to a smaller amount, VaR is rejected; recompute with a smaller `tol`.
Examples
value_at_risk(c(0, 100, 100, 300), level = c(0.5, 0.9))
#> # A tibble: 2 × 3
#> level value_at_risk method
#> <dbl> <dbl> <chr>
#> 1 0.5 100 empirical_simulation
#> 2 0.9 300 empirical_simulation
value_at_risk(severity_spec("exponential", rate = 0.01), level = 0.95)
#> # A tibble: 1 × 3
#> level value_at_risk method
#> <dbl> <dbl> <chr>
#> 1 0.95 300. exact_quantile