Actuarial central estimate

The US Actuarial Standards Board defines the actuarial central estimate in ASOP 43, "Property/Casualty Unpaid Claim Estimates," as an estimate that represents an expected value over the range of reasonably possible outcomes. The word that matters is reasonably: the standard says that range may leave out conceivable extreme events whose contribution to the expected value cannot be reliably estimated. So a central estimate can sit below the true mean of a heavy-tailed distribution. The actuary builds it from several methods, chain ladder, Bornhuetter-Ferguson, frequency and severity, then selects one value per accident year, and that weighted choice is documented judgment more than calculation. Australia built a stricter regime on top of it. Since the reform that followed HIH's collapse in March 2001, APRA has required insurers to hold the central estimate plus a risk margin targeting a 75% probability of sufficiency. The total cannot fall below a floor usually described as half a standard deviation above the central estimate. Solvency II starts from a similar logic: the best estimate of Article 77 of the 2009 directive is also a probability-weighted mean. But it discounts cash flows at the risk-free curve, includes expenses and keeps the risk margin separate, calculated on a cost of capital basis. French statutory accounts follow another rule: the claims reserve is the estimated value of the outlays needed to settle claims incurred, undiscounted except for annuities. The prudence principle pushes it toward the upper end of the range. Three numbers for the same book, then, and a comparison that only makes sense once the framework is named. Not to be confused with the risk margin, which is added to the central estimate, or with the actuarial opinion on reserves, which comments on it.