Proportional Reinsurance Retained Variance Calculator
Calculate retained aggregate-loss variance after proportional reinsurance by multiplying total variance by the square of the retained share.
Description
Calculate retained aggregate-loss variance after a fixed proportional cession using the square of the retained share.
Proportional Reinsurance Retained Variance helps you calculate retained aggregate-loss variance after a fixed proportional cession using the square of the retained share.
Use this calculator when every covered loss is multiplied by the same retained proportion, as in a simplified quota-share arrangement. It shows how linear scaling of losses changes variance.
When to use Proportional Reinsurance Retained Variance
Use this calculator when every covered loss is multiplied by the same retained proportion, as in a simplified quota-share arrangement. It shows how linear scaling of losses changes variance.1
How the calculation works
If retained losses equal the original losses multiplied by r, the variance is multiplied by r squared. The retained share is one minus the ceded share, so the calculation follows directly from the variance scaling identity.2
Var(retained losses) = (1 − c)^2 × Var(total losses) 1Inputs and interpretation
Enter c as a decimal share from zero to one and total variance in squared currency units. A zero cession retains all variance; a full cession leaves zero retained variance.
Limitations and assumptions
The formula applies to a fixed proportional transformation. It is not valid for excess-of-loss, stop-loss, caps, deductibles, variable commissions, coverage exclusions, or other nonlinear reinsurance structures.
References
-
The Effect of Trend on Excess of Loss Coverage — Casualty Actuarial Society
-
Actuarial science — Wikipedia contributors
Similar or alternative tools
- Compound Poisson Total Variance Calculator
Calculate the variance of aggregate claims for a compound Poisson model as the claim frequency times the second moment of severity.
- Aggregate Excess Loss Layer Calculator
Calculate the aggregate loss falling within a layer above an attachment point, capped by the layer limit.
- Buhlmann-Straub Credibility Factor Calculator
Weight experience against the prior mean using the Buhlmann-Straub credibility factor from total exposure and the variance components.