Simulation Methods for Aggregate Loss Models
Learn simulation techniques for modeling aggregate losses and estimating risk measures on Exam STAM.
Monte Carlo Simulation
When analytical methods are intractable, Monte Carlo simulation provides aggregate loss distribution estimates. The procedure is: (1) generate a random claim count N from the frequency distribution, (2) generate N independent claim amounts from the severity distribution, (3) sum the claims to get one realization of aggregate loss S. Repeating this thousands of times builds an empirical distribution of S. The inverse transform method generates random variates by applying the inverse CDF to uniform random numbers.
Estimating Risk Measures
From simulated aggregate losses, you can estimate any distributional quantity. The sample mean estimates E[S], percentiles estimate VaR, and the average of simulated values exceeding VaR estimates TVaR. Stop-loss premiums are estimated as the mean of max(S-d, 0). The standard error of simulated estimates decreases proportionally to 1/sqrt(n), where n is the number of simulations. Variance reduction techniques like importance sampling and control variates can improve efficiency. Exam STAM focuses on the basic simulation algorithm and interpreting simulation output.