Net stop-loss premium

Computes E[(X-d)+], the expected excess loss over retention d, with no loading or discounting. This is a per-risk expectation for X. Equivalently, the premium is the integral of the survival function from the retention to infinity, provided the expectation is finite.

Usage

stop_loss_premium(x, retention = 0, value = NULL)

Arguments

x

A nonnegative loss sample or simulation tibble, a supported severity specification, or an aggregate-distribution result.

retention

Finite nonnegative retention amount(s).

value

Optional name of a loss column when `x` is a data frame.

Value

A tibble with `retention`, `premium`, and `method`.

Details

Closed forms are available for exponential, gamma, lognormal, Weibull, and Pareto II severity. Burr XII, log-logistic, and bounded custom distributions with a survival provider use explicitly identified numerical integration of the survival function. Finite discrete models and observations are summed exactly over their mass distributions. A missing aggregate tail forbids an exact stop-loss expectation; no renormalization or zero assumption is made. The Pareto II premium is infinite when shape <= 1. Per-loss exponential severities transformed by [apply_coverage()] use closed forms for ordinary and franchise deductibles, including unlimited coverage. This avoids numerical integration over very large limits.

Examples

stop_loss_premium(c(0, 100, 200, 500), retention = c(0, 150))
#> # A tibble: 2 × 3
#>   retention premium method              
#>       <dbl>   <dbl> <chr>               
#> 1         0     200 empirical_simulation
#> 2       150     100 empirical_simulation
stop_loss_premium(severity_spec("exponential", rate = 0.01), retention = 50)
#> # A tibble: 1 × 3
#>   retention premium method     
#>       <dbl>   <dbl> <chr>      
#> 1        50    60.7 closed_form