Constant tail factor

A given factor from the attachment age to ultimate, as chainladder-python's TailConstant. Past the oldest age the factor is spread over the following periods as 1 + x * decay^k, the last factor making up the difference; this shapes the factors past the attachment (chain_ladder_fit's tail_ldf), not the factor to ultimate. An attachment before the oldest age replaces the estimated factors from there. A plain number given as tail to chain_ladder() or mack() is tail_constant(tail).

Usage

tail_constant(factor = 1, decay = 0.5, attachment_age = NULL)

Arguments

factor

Factor from the attachment age to ultimate; finite and positive (checked when the tail is fitted).

decay

Share of each period's development kept in the next, from 0 to 1.

attachment_age

Age in months the factor attaches at (the first age at or after it), or NULL for the oldest age. An age at or before the youngest replaces every estimated factor (chainladder-python ignores such an attachment).

Value

A tail_constant object.

Details

Properties: factor, decay and attachment_age (NULL for the oldest age).

See also

tail_curve(), tail_bondy(), tail_log_linear().

Examples

long <- data.frame(year = rep(2018:2021, 4:1),
                   age = c(12, 24, 36, 48, 12, 24, 36, 12, 24, 12),
                   paid = c(100, 150, 165, 170, 110, 170, 180, 120, 175, 130))
tri <- triangle(long, "year", "age", "paid")
fit <- chain_ladder(tri, tail = tail_constant(1.05, attachment_age = 36))
fit@ldf
#>    12-24    24-36    36-48 
#> 1.500000 1.078125 1.024011 
fit@tail
#> [1] 1.02538
fit@tail_ldf
#> [1] 1.012005 1.013216