Vectorized helper function for applying the tail method. Melts down payment from first tail year to desired development year.
Usage
tail_factor(dev_year, start_of_tail, end_of_tail)
Arguments
- dev_year
desired development year
- start_of_tail
development year of tail start
- end_of_tail
development year of tail end
Value
numeric factor to apply to payment in first tail year
Details
As data becomes thin in later development years, for each reserve class all payments between start_of_tail and end_of_tail are grouped and therefore scaled to the year start_of_tail and vice versa by
$$Z_{M+j} = Z_{M+1} \cdot \frac{T - M - j + 1}{T - M}, \quad j = 1, \ldots, T-M$$
Examples
tail_factor(25, 17, 50)
#> [1] 0.7647059
tail_factor(17, 17, 50)
#> [1] 1
tail_factor(50, 17, 50)
#> [1] 0.02941176