Scaling

The scaling component multiplies every loss by a constant factor $f$:

$$L^{\text{gross}} = f \cdot L^{\text{subject}}$$

This single operation serves two distinct business purposes:

• Cession percentage ($f = q$) — the proportion of every loss that the cedent transfers to the reinsurer, as in a quota share
• Participation share ($f = p$) — the reinsurer’s share of a layer, used when multiple reinsurers split an excess-of-loss contract

The mathematics are identical. The business context determines what the factor means.

Applied to Trial 9 at $f = 0.25$, every occurrence shrinks to a quarter of its subject loss — the shape of the year is unchanged, only the magnitude:

Earthquake Hurricane

Scaling Trial 9 by 0.25. Every bar is a quarter of its subject height; the $102.4M September hurricane becomes $25.6M, the $80.8M October storm $20.2M.

Occurrence / total	Subject	Gross (×0.25)
Sep 6 — FL hurricane	$102.4M	$25.6M
Oct 5 — FL hurricane	$80.8M	$20.2M
Trial 9 total	$272.1M	$68.0M

helios_re/scale.py Python

▶ Run Reset

Across all 20 trials, the gross curve is the subject curve scaled vertically by 0.25 at every return period:

Scaling EP curves: SunCoast subject vs 25% of every loss. The gross curve is a vertical scaling of the subject — the distribution's shape is preserved.

Key Insight

Scaling preserves the shape of the loss distribution — only the magnitude changes. Every metric scales linearly: EL by $f$, VaR by $f$, TVaR by $f$. This linearity makes scaling the simplest building block to reason about and the easiest to optimize in a computational pipeline.

Scaling is the final term in nearly every contract — the quota share cession and the CatXoL participation are both this one operation.