Confusing ordinary and franchise deductibles

With an ordinary deductible d, the insurer pays X - d when X > d. With a franchise deductible d, the insurer pays X (the full amount) when X > d. The expected payment formulas are different and using the wrong one changes your answer significantly.

Using the wrong Panjer recursion starting value

For the (a,b,0) class, the recursion starts with P(0) computed from the primary distribution. For the (a,b,1) class (zero-truncated), P(0) = 0. Starting with the wrong value propagates errors through the entire recursion.

Mixing up per-loss and per-payment formulas

E[Y^L] = E[(X-d)+] = E[X] - E[X ^ d] includes payments of zero (when X < d). E[Y^P] = E[Y^L] / (1 - F(d)) conditions on a payment occurring. The exam tests both, and using the wrong one is a frequent error.

Forgetting inflation in severity adjustments

When trending losses, you must apply the inflation factor to the distribution parameter, not to the final answer. For a Pareto distribution with inflation, the scale parameter shifts, not the shape parameter.

Errors in loss development factor selection

When computing development factors from a triangle, candidates sometimes confuse age-to-age factors with cumulative development factors. The ultimate loss is the latest diagonal times the tail factor, not the individual age-to-age factors.

Incorrect credibility weight calculation

In Buhlmann credibility, Z = n/(n+k) where k = v/a (EVPV divided by VHM). Swapping the numerator and denominator in k gives Z that is too large or too small, and the credibility estimate shifts accordingly.

Not adjusting premiums to current rate level

Ratemaking requires on-level premiums. If rate changes occurred during the experience period, you must adjust each policy period to the current rate level before computing the loss ratio.

Confusing IBNR with case reserves

IBNR (Incurred But Not Reported) reserves are for claims that have occurred but have not yet been reported. Case reserves are for reported claims. Total reserves are IBNR plus case reserve development. Treating these as interchangeable produces wrong reserve estimates.

Applying the wrong credibility model

Buhlmann assumes equal exposures across periods. Buhlmann-Straub allows varying exposures. Using Buhlmann when exposures differ across periods ignores important information and gives a suboptimal credibility estimate.

Arithmetic errors in aggregate loss calculations

Computing the mean and variance of aggregate losses requires two separate formulas. E[S] = E[N]*E[X] and Var(S) = E[N]*Var(X) + Var(N)*(E[X])^2. Missing the second term in the variance formula is very common.

Common STAM Mistakes