Policy Limit Effect Calculator

Work out policy limit effect instantly with clear inputs, formula shown and shareable results.

About Policy Limit Effect Calculator

A policy limit caps the insurer's payment per claim. With exponential severities the limited expected value is μ(1 − e^(−L/μ)), which shows how quickly extra limit stops buying much expected cover once L is a few multiples of the mean.

Formula

Limited expected value

E[min(X,L)] = μ(1 - e^(-L/μ))

μ: Mean severity
L: Policy limit

Worked example

With the default values below, Policy Limit Effect Calculator returns Expected Loss Within The Limit of $2,314,382.42. Change any input above and every figure here is recalculated in your browser.

Inputs used

Mean Claim Severityminimum 0: 30,000
Policy Limitminimum 0: 100,000
Expected Claim Countaccepts 0.1–100,000: 80

Results

Expected Loss Within The Limit: $2,314,382.42
Expected Loss Above The Limit: $85,617.58
Increased Limit Factor Achieved: 96.433%
Probability A Claim Exceeds The Limit: 3.5674%

Step by step

1Values used
2Limited expected value
3Expected Loss Within The Limit= 2,314,382.42
4Expected Loss Above The Limit= 85,617.58
5Increased Limit Factor Achieved= 96.433
6Probability A Claim Exceeds The Limit= 3.5674

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does doubling the limit not double the premium?

Because only the thin tail beyond the old limit is added. Increased limit factors rise steeply at first and then flatten.

Does the tail matter?

Yes — with heavier-tailed severities than exponential, high limits cost considerably more than this model suggests.