Frequency, severity and retention modelling for an HNW home book

Case study described in general terms. It contains no proprietary data, relativities or model outputs.

The problem

High-net-worth home portfolios have few policies, high sums insured and claims that are dominated by a handful of large losses. The usual personal-lines approach of fitting a GLM on plenty of data and reading off the relativities doesn’t work well here. Credibility is thin, the tail drives the loss cost, and underwriters need to understand every rating factor.

Approach

• Frequency and severity separately. I fitted Poisson frequency and Gamma severity GLMs as the interpretable baseline, then GBMs to find interactions and non-linearities the GLM missed.
• Large-loss treatment. Attritional claims were capped at a threshold, and the loading for losses above it was allocated separately. Severity was fitted as a truncated distribution where excess-of-deductible data required it.
• Retention model. I built a renewal-probability model alongside the cost model so that proposed rate changes could be read against their likely effect on lapses.
• Explainability. SHAP values translated GBM behaviour into factor-level views that underwriters could challenge, and they guided which GBM signals were promoted into the GLM.
• Reinsurance. Loss costs were adjusted for the layers the program retains.

Outcome

• TODO: what changed as a result
• TODO: what you’d do differently next time