Loss ratio SE: ratio_se = SE(L/P) — .compute_ratio

Ratio-specific internal helper. Two variants:

"fixed" (default): Premium treated as fixed (non-random). \(\mathrm{SE}(L/P) = \mathrm{SE}(L) / P\). Strictly a degenerate case of the delta method with Var(P) = 0 and Cov(L,P) = 0.
"delta": First-order Taylor (delta method) including premium uncertainty and loss-premium correlation rho: \(\mathrm{Var}(L/P) \approx (\mathrm{SE}(L)/P)^2 + (L \cdot \mathrm{SE}(P) / P^2)^2 - 2 \rho L \mathrm{SE}(L) \mathrm{SE}(P) / P^3\). The variance is clipped at zero before the square root (high rho can drive the linearised estimate negative).

Not exported; called only by fit_ratio(). The "fixed" branch encodes the actuarial assumption that earned premium is known (not estimated), so this helper is not a generic ratio-SE utility.

Usage

.compute_ratio_se(
  loss,
  premium,
  loss_se,
  premium_se = NULL,
  method = c("fixed", "delta"),
  rho = 0.95
)

Arguments

loss: Ultimate loss vector (L).
premium: Ultimate premium vector (E).
loss_se: SE(L).
premium_se: SE(P). Unused for "fixed"; may be NULL.
method: One of "fixed" (default) or "delta".
rho: Loss-premium correlation in (-1, 1). Used only for "delta". Default 0.95.

Value

A numeric vector the same length as loss.