Guide 2 · the actuarial side

How a captive is funded

A captive’s premium has to cover the losses it expects, the share it passes to reinsurers, a margin for bad years, and its running costs. The first three are actuarial questions. Move the sliders to see how they work.

Illustration only: a claim-size curve shaped like US general-liability claims in Verisk’s published data1, and 30 claims a year. The captive design tool uses your own numbers.

1 of 3 · claim sizes

Most claims are small. A few are enormous.

Claim sizes follow a skewed curve, commonly modelled as lognormal3. Half of all claims here are below the median, but the rare large ones pull the average far higher. That gap is why a captive can’t be funded on a typical claim.

median $8K
mean $60K
retention $100K
$100$1K$10K$100K$1M
Claim size (log scale). Highlighted claims sit inside the captive’s retention; grey ones run past it.
2 of 3 · retention

The captive keeps the first slice of every claim.

Above the retention, a reinsurer pays. Raise the retention and the captive keeps more of the expected losses, and pays less for reinsurance.

$25K$50K$100K$250K$500K
40% kept
60% to reinsurer
expected kept per claim, lognormal2
E[min(X, R)] = eμ+σ²/2·Φ((ln R − μ − σ²)/σ) + R·[1 − Φ((ln R − μ)/σ)]
μ = 9.0 · σ = 2.0 · R = $100K
E[min(X, R)] = $24K of an average claim of $60K
3 of 3 · the margin for bad years

Fund for a bad year, not an average one.

The number of claims and their sizes both vary, so a year’s kept losses swing around their average. Actuaries offer a range of confidence levels, with expected losses at about the 50th to 55th percentile4. Captives commonly fund above that: one actuarial paper works an example at 75% and notes a start-up captive writing volatile cover would typically fund at 90%3. The chart simulates 4,000 years of claims.

$724K
expected kept losses a year
$860K
funded at 75% confidence
+$136K
margin for bad years (19% above expected)
expected
75% funded
Each bar is how often a year’s kept losses land in that range. Grey years cost more than the funded amount; that is what capital is for.

This is the method. The tool runs it on your data.

Realtech’s captive design tool uses a claim-size curve for each line of cover, adjusted for your own claims history, and sets out the kept losses, reinsurance and running costs for your stores.

Sources and method

  1. Claim-size curve: lognormal with μ = 9.0, σ = 2.0 (median ≈ $8,100, mean ≈ $59,900). It sits within lognormal fits we made to the size-of-loss distribution in Verisk, 2024 Executive Insights: General Liability (Q2 2019–Q1 2024; bodily injury μ ≈ 9.4, σ ≈ 1.9; property damage μ ≈ 8.3, σ ≈ 1.7; indemnity before development and expenses). verisk.com Statistical-agent data; the fit is our calculation.
  2. Limited expected value of the lognormal, the standard closed form. Checked against 2 million simulated claims (agreement within 0.1%). Standard actuarial result.
  3. A. M. Conway (Tillinghast–Towers Perrin), “Ratemaking for Captives and Alternative Market Vehicles,” Casualty Actuarial Society Forum, Winter 2005: funding at 75% and 90% confidence; Poisson claim counts and lognormal claim sizes for simulation. casact.org Actuarial literature, dated.
  4. D. Riggin, “Captive Underwriting Profits—without Third-Party Business,” IRMI: confidence levels; expected losses normally at the 50th or 55th percentile. irmi.com Industry reference.

Simulation, following the approach in source 3: claims per year drawn as Poisson with a mean of 30, claim sizes from the curve above, each claim capped at the retention; a fixed random seed keeps the chart stable. This guide is general information, not insurance, legal or tax advice. Realtech does not sell insurance.