Insurance calculators
Deductibles, limits and layers
Expected payment per loss and per payment, loss elimination ratio, increased limits factors and layer costs for lognormal, Pareto and exponential claims.
Inputs
Results
Expected payment per loss
18,863.49
Mean claim 25,000.00
Expected payment per payment
28,156.97
67.0% of losses exceed d
Loss elimination ratio
16.63%
Saved by the deductible
Increased limits factor
1.1609
At u against 100,000.00
Increased limits factor by policy limit
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Methodology
Conventions
- Severity is set by its mean and coefficient of variation. The lognormal follows from them directly, the Pareto is the two-parameter (Lomax) form (it needs a CV above 100%), and the exponential has a CV of 100%.
- The insurer pays coinsurance × (min(X, u) − min(X, d)) for a deductible d and a maximum covered loss u.
References
- Klugman, Panjer and Willmot, Loss Models: From Data to Decisions, 5th ed.
Formulas
- Per loss
- E[Y^L] = \alpha\,(E[X\wedge u] - E[X\wedge d])
- Per payment
- E[Y^P] = E[Y^L] / S(d)
- Loss elimination ratio
- LER = E[X\wedge d] / E[X]
- Increased limits factor
- ILF(u) = E[X\wedge u] / E[X\wedge b]
- Lognormal
- E[X\wedge u] = e^{\mu+\sigma^2/2}\Phi\!\big(\tfrac{\ln u - \mu - \sigma^2}{\sigma}\big) + u\big(1 - \Phi(\tfrac{\ln u - \mu}{\sigma})\big)
- Pareto
- E[X\wedge u] = \tfrac{\theta}{\alpha-1}\Big(1 - \big(\tfrac{\theta}{\theta+u}\big)^{\alpha-1}\Big)