Statistics for Risk Modeling (SRM) Exam
Regression and risk modeling
Statistics for Risk Modeling emphasizes applying statistical models to insurance and risk problems. Know simple and multiple linear regression, least squares, coefficient interpretation, inference, residual diagnostics, and model selection. Extend to generalized linear models, especially Poisson and gamma with log links, and understand deviance, dispersion, and exposure offsets. Time series topics include stationarity, autocorrelation, and ARIMA intuition. Risk measures such as VaR and TVaR require understanding tails, not just averages.
Validation traps
Do not interpret a regression coefficient causally unless the design supports it. Watch for omitted variables, multicollinearity, extrapolation, and overfitting. In GLMs, check the link function and variance function; a log link models the log mean, not the mean. For model comparison, use out-of-sample or information criteria rather than training fit alone. For VaR, remember it is a quantile and says nothing about the size of losses beyond it; TVaR averages those tail losses.
Worked rule
In a log-link Poisson model with exposure offset, predicted claim frequency is exp(beta0 + beta1 x)/exposure, or equivalently the mean count is exposure times exp(linear predictor). If beta1 = 0.2, a one-unit increase in x multiplies expected frequency by e^0.2 = 1.221, a 22.1% increase. The trap is adding 0.2 to the mean rather than exponentiating. Always state the scale of the response.