Monte Carlo Insurance Loss Simulator

Monte Carlo Insurance Loss Simulator

OVERVIEW

This tool simulates the aggregate annual losses of an auto insurance portfolio using a compound probability model. You set the portfolio parameters — number of drivers, claim probability, and severity range — and the simulator runs thousands of independent one-year scenarios to estimate the distribution of total losses.

The key output is the solvency reserve: the amount an insurer must hold to cover losses with 95% confidence. Two methods are compared side by side — a closed-form analytical estimate (via the Central Limit Theorem) and an empirical estimate drawn directly from the simulated distribution.

THE MODEL

• Claim frequency — each driver independently files a claim with probability p, so the number of claims follows a Binomial(N, p) distribution.
• Claim severity — each individual claim amount is drawn from a Uniform(min, max) distribution, representing a plausible range of loss costs.
• Aggregate loss — total portfolio loss S is the sum of all individual claim amounts, a compound random variable whose moments follow from the Law of Total Expectation and Variance.
• CLT reserve — for large portfolios the CLT approximates S as Normal(E[S], Var[S]), giving a closed-form 95th-percentile reserve: E[S] + 1.645·Std[S].

WHY THIS MATTERS

Actuaries use models like this to set premium rates and statutory reserves. The gap between the CLT reserve and the empirical reserve reveals how well the normal approximation holds — an important check for portfolios with heavy-tailed or skewed severity distributions.

PARAMETERS

• Drivers (N) — the total number of policyholders in the portfolio. Larger portfolios produce tighter, more bell-shaped loss distributions as individual randomness averages out.
• P(claim) — the annual probability that any single driver files a claim. At 5%, roughly 500 of 10,000 drivers are expected to have a loss in a given year.
• Min Severity — the lower bound of the Uniform claim cost distribution. No individual claim is assumed to cost less than this amount.
• Max Severity — the upper bound of the Uniform claim cost distribution. Widening the severity range increases aggregate variance and pushes the required reserve higher.
• Simulations — the number of independent one-year scenarios generated. More simulations reduce sampling noise in the empirical reserve estimate; 10,000 is sufficient for stable results at most parameter settings.
• Premium Loading — a markup applied on top of expected losses to cover expenses and profit. At 20% loading, an insurer collecting $1.20 for every $1.00 of expected loss targets an 83% loss ratio. Adjusting this slider shows how pricing decisions interact with the reserve requirement.

PREMIUM CALCULATOR

Once the simulation runs, the tool applies the loading factor to derive two pricing outputs. Premium per driver is the annual rate each policyholder would be charged: (E[S] / N) × (1 + loading). Total premium pool is the aggregate revenue collected across the portfolio: E[S] × (1 + loading). Together these show whether the premium structure is sufficient to cover both expected losses and the solvency reserve — the central question in actuarial rate-setting.