Description: A significant fraction of insurance risk is characterized by the tail of the claims distribution, where we have much less data to model probabilities accurately. Ignoring the tails can lead to underpricing of tail risk and mispricing. Estimation of the tails can be complex due to a bias-variance tradeoff--the further out we go into the tail the more accurately we can model the extreme tail (lower bias) but the less data we have (increased variance). The statistical tools of Extreme Value Theory can be leveraged to more accurately estimate both the incidence and the severity of extreme events given that they occur. using the Generalized Pareto Distribution.

Description: Health claims are not normally distributed. Claims Forecasting can be improved by understanding the entire distribution of plausible values of future claims, for example knowing there is an 80% chance future claims are between $340 and $375 PMPM. Confidence intervals around our estimates allow us to understand for each range around the best estimate (for example +/- 1%) what is the probability that future claims will fall in that range. Quantile Regression is a mathematical technique where you can estimate any percentile of the claims distribution you are looking for as a function of demographics, diagnosis indicators, prior cost variables, or other significant predictors. You can see which coefficients are important at different parts of the distribution. Individual and group distributions can be constructed. There are numerous applications in pricing and underwriting, stop loss, provider profiling, ACO target setting, allocation of group risk charges based on volatility, discounting strategy, and experience analysis.

Description: Traditional risk scoring models include only fixed (non-random) demographic and condition-based variables. By including the provider effect as part of the risk scoring model as a random effect, we can get better estimates of provider performance (incorporating practice patterns conditional on patient morbidity profile). This approach can be generalized to study other factors that are now masked in error variance (i.e. area, Social Determinants) but if modeled could give us better estimates of risk