Limited expected value, stop-loss and layer

lev(dist, limit) is E[min(X, limit)]; stop_loss(dist, retention) is E[max(X - retention, 0)], computed directly so it stays accurate far into the tail; layer(dist, limit, attachment) is the expected loss to the layer limit xs attachment. Defined for lognormal and grid_distribution severities and the Pareto family (pareto, piecewise_pareto, log_affine_pareto, generalized_pareto).

Usage

lev(dist, limit, ...)

stop_loss(dist, retention, ...)

layer(dist, limit, attachment, ...)

Arguments

dist

A severity.

limit, retention

Numeric vector.

...

Unused; for methods.

attachment

Layer attachment, a single number.

Value

A numeric vector (lev, stop_loss) or a single number (layer).

Examples

d <- lognormal(7, 0.5)
lev(d, c(500, 1500))
#> [1]  494.7876 1082.1092
stop_loss(d, 1500)
#> [1] 160.5389
layer(d, 1000, 500)
#> [1] 587.3217