Reinsurance tower on the aggregate grid
tower_on_grid.RdExact annual distributions of gross, each layer's ceded loss and net, by
FFT, with no sampling error. Each layer's per-occurrence recoveries form a
severity grid, which is compounded with the same claim count; annual terms
and the share then apply to the total. With attachments, limits and annual
terms on multiples of the step, the grids are exact for the discretized
problem. Otherwise losses between points are split between their
neighbours: means stay exact and on_points is FALSE.
Value
A list with gross (a grid_distribution whose report
describes the compound calculation), ceded (a named list of
grid_distributions at the placed share; a share c gives step
c * step), net (a grid_distribution or NULL),
expected_reinstatement_premium (named, 0 without paid reinstatements)
and on_points.
Details
The grids are marginal: use apply_tower() on simulated events for joint
results. net is given when no layer has annual terms, or when the last
stage is a single aggregate cover such as an aggregate_stop_loss(); otherwise it is
NULL. A tower whose annual terms inure to a later stage is rejected,
because those terms depend on event order.
Examples
sev <- grid_distribution(1, c(0, 0.4, 0.3, 0.2, 0.1))
tw <- reinsurance_tower(list(xol_layer("2x2", 2, 2)))
r <- tower_on_grid(tw, poisson_count(3), sev, points = 200)
mean(r$ceded[["2x2"]])
#> [1] 1.2
r$on_points
#> [1] TRUE