CAS Exam 5 cheat sheet

Written premium is recorded at policy inception for the full term; earned premium recognizes exposure as coverage is consumed. Unearned premium reserve equals the portion of written premium not yet earned.

Exposure base converts heterogeneous risks to a common unit (car-years, payroll per $100, sales per $1,000). Rate = loss cost / (1 - expense ratio - profit/contingency load) when expenses are variable to premium.

Loss ratio method: indicated rate change = (incurred losses + LAE) / (earned premium x permissible loss ratio) - 1, applied to current rates. Pure premium method: indicated average rate = (incurred losses + LAE) / exposure units, then grossed up by permissible loss ratio.

On-level premium adjustment multiplies historical premium by a parallelogram factor so all premium reflects current rate level; the factor is the ratio of current rate level to the average level during the experience period.

Trend factors extrapolate frequency and severity to the future policy period midpoint; trended loss cost = historical loss cost x frequency trend x severity trend, each raised to the number of periods to the average accident date.

Credibility weights the subject experience Z against the complement of credibility (1 - Z), typically the class loss cost. Limited fluctuation credibility sets Z = sqrt(n / n_full) capped at 1, where n_full is the exposure needed for full credibility.

Loss development factors adjust incurred losses from the experience period to an ultimate basis before trending; the product of age-to-ultimate factors applied to reported losses yields ultimate losses.

Expense categories: fixed expenses per exposure unit, variable expenses proportional to premium, and loss-based assessments. Only variable-to-premium expenses enter the permissible loss ratio denominator as a premium-proportional load.

Case reserves are set claim-by-claim by adjusters; IBNR covers claims not yet reported plus development on known claims. Total unpaid = case reserves + IBNR (plus a possible IBNER component depending on convention).

Chain-ladder development: age-to-age factor = cumulative losses at age j+1 / cumulative losses at age j. Multiply reported losses by the product of remaining factors to estimate ultimate.

Bornhuetter-Ferguson estimate = reported losses + expected unreported losses x (1 - 1/development factor). It blends reported development with an a priori expected loss ratio, giving stability for immature years.

Expected loss method (a priori): ultimate = earned premium x expected loss ratio, used when reported data are too thin to support development.

Mack chain-ladder provides a distribution-free estimate of the standard error of the chain-ladder reserve by combining process and parameter variance across development periods.

Paid versus incurred development: paid triangles respond to settlement speed and case-reserve adequacy; incurred triangles embed adjuster reserve changes. Divergence between the two signals changing case-strength.

Tail factor extends development beyond the oldest observed age; it is often fit with an inverse power curve or exponential decay to the selected ultimate.

Berquist-Sherman adjustments restate historical data for changes in case-reserve adequacy or settlement rates before applying development methods, so the triangle reflects current conditions.

Discounting of reserves applies a present-value factor to expected payment timing; undiscounted reserves are the default for most statutory reporting, with discounting used for certain long-tailed lines.