Predictive Analytics

Study guides: Exam PA, Exam ATPA, Exam DISC-DA, Exam 5, Exam PCPA, Exam 6U, Exam 8, Exam GH-301

Predictive Analytics is the practice of fitting a statistical model to historical data so that it can predict an outcome for cases it has not seen — the expected loss cost of a policy being quoted, the chance a claim turns litigated, the probability a customer renews. In P&C insurance the workhorse is the Generalized Linear Model, and the discipline is as much about the data and the communication around the model as about the fit itself.

$\hat{y} = \hat{f}(\mathbf{x})$

$g\big(E[Y \mid \mathbf{x}]\big) = \beta_0 + \beta_1 x_1 + \cdots + \beta_p x_p$

$Y$ is the target (response) — claim count, claim severity, pure premium, a yes/no event; $\mathbf{x}$ are the predictors (rating variables, policy and claim characteristics); $\hat{f}$ is the fitted model. The second line is the GLM form of $\hat{f}$ , with link $g$
The workflow the CAS PCPA requirement is built around: frame the business problem → select and review the data (Data Quality) → explore it (Exploratory Data Analysis), fix missing values and outliers, transform variables → split off a hold-out sample → fit, diagnose and refine the model → validate on data it has not seen → interpret and communicate the result
Supervised methods (GLMs, trees) learn from a known target; unsupervised methods (clustering) find structure with no target. Pricing and claims models are supervised
A prediction is only as good as its out-of-sample performance: in-sample fit always improves as terms are added, so a model is judged on hold-out data or by Cross-Validation (see Bias-Variance Tradeoff)
In the US, two actuarial standards of practice govern the work: ASOP No. 23 (Data Quality) and ASOP No. 56 (Modeling)

Building a Pure Premium from Two Models A frequency model (Poisson, log link) predicts $0.06$ claims per car-year for a risk, and a severity model (Gamma, log link) predicts an average claim of $\$7{,}500$ . What is the predicted pure premium, and why fit two models rather than one?
Answer
 $\begin{align*} \text{Pure premium} &= \text{Frequency} \times \text{Severity} \\ &= 0.06 \times 7{,}500 \\ &= \$450 \text{ per car-year} \end{align*}$ 
Splitting the target lets each model use the distribution that suits it (counts vs. positive, skewed amounts) and shows why a risk is expensive — a variable can drive frequency without moving severity. A single Tweedie pure-premium model is the one-model alternative.

Framing the Business Problem A commercial auto insurer asks for "a model of our worst accounts." Before any data is touched, what must be settled?

Answer The target — "worst" could mean highest loss ratio, highest claim frequency, or largest single loss, and each gives a different model. The unit of analysis — policy, vehicle, or policy-year. The decision the model feeds — a rate change, an underwriting referral, a non-renewal — which fixes how the output must be presented and which variables may lawfully be used. And the validation — what hold-out data will show the model works. Settling these first is what makes the rest of the project answerable.