Part 17: Limitations
Part 17: Limitations¶
This section is honest about what the approach cannot do. Understanding the limitations is as important as understanding the method.
1. Factor adjustments are uniform within each factor. The optimiser scales every level of the age factor by the same multiplier. It cannot say "increase the 17-21 band by 8% and the 25-29 band by 2%." Reshaping factor relativities — changing the gradient of the NCD discount schedule, widening the age relativities, re-tiering vehicle groups — requires a separate modelling exercise with its own regulatory justification. The optimiser handles only the scale of uniform rate actions.
2. The demand model is almost certainly miscalibrated. The logistic demand model assumes a constant price elasticity across the entire portfolio. In practice, elasticity varies by channel, tenure, competitive position, policy age, and geography. A 19-year-old shopping on a PCW will respond differently to a 5% price increase than a 55-year-old who has never visited a PCW. Using a single price coefficient for the whole portfolio introduces systematic error into the LR and volume projections. The correct approach is a policy-level demand model, ideally a CatBoost binary classifier predicting renewal probability as a function of price ratio and all other policy characteristics. The rate-optimiser library accepts any callable in place of the logistic demand function — replacing it with a CatBoost model is a straightforward extension.
3. The normal approximation in the stochastic extension is not appropriate for small or concentrated books. The CLT-based normal approximation for portfolio LR holds well for diversified books with 50,000+ policies and no dominant individual risks. For smaller books, or books with large commercial exposures, the tail of the loss distribution is far from normal and the 90th percentile LR implied by the chance constraint will be understated. Use simulation for those cases.
4. ENBP applies at the point of quote, not the point of the factor table. The constraint as implemented compares the adjusted renewal premium against the NB equivalent computed from the same factor tables. In practice, the NB equivalent is the live quoted price at the time of renewal — which may differ if the market has moved, if the NB quote includes channel-specific terms, or if introductory discounts vary between NB and renewal. For a regulatory compliance check, the actual NB quote from the PCW or direct quote engine should be used, not the factor-table approximation.
5. The multi-period effects of a persistent NB/renewal price gap are not modelled. The optimiser takes renewal volume as the primary volume metric and ignores new business volume. A rate action that creates or widens a gap between NB prices and renewal prices does not breach ENBP (as long as renewal prices are below or equal to NB prices), but it changes the book composition over time. If NB comes in at significantly lower rates than in-force renewals, the average renewal rate increases and the average NB rate decreases. Over 3-5 years, this shifts the book's risk profile (newer, cheaper customers are more likely to be better risks) and makes the historical LR a poor predictor of future LR. The optimiser does not model this. A multi-period simulation is needed to capture it.
6. The minimum-dislocation objective treats all factors symmetrically. A 1pp increase in the age factor is penalised the same as a 1pp increase in the tenure discount, even though the customer impact is different: the age factor affects all customers (including new business), while the tenure discount affects only renewals. If the underwriting director wants to prioritise rate action on specific factors, encode this as asymmetric factor bounds (wider on the factors you want to move more, narrower on those you want to protect) rather than modifying the objective function.
7. The solver does not account for competitive response. The demand model uses a fixed market premium as the benchmark. In practice, if you take a 15% rate increase, competitors may respond — raising their own rates (which reduces your lapse risk) or holding rates (which increases it). The market premium is not fixed. The demand model is correct given the assumption of no competitive response; whether that assumption is reasonable depends on the pricing cycle and your market position.
8. Factor-bound infeasibility is not always resolvable within the pricing review. If the LR target cannot be achieved within the approved factor caps without breaching the volume floor, the correct response is to escalate — not to relax the constraints silently. The escalation question for the underwriting director is: "We need a 4.5% rate increase but the approved cap is 4%. Which do you prefer: widen the cap, accept a higher LR target, or accept a lower volume floor?" Making this trade-off explicit is one of the main governance benefits of the optimisation framework.
Summary¶
Rate optimisation is, at its core, a search problem that your Excel spreadsheet solves badly. The rate-optimiser library solves it formally: given your constraints, find the factor adjustment vector with the smallest total customer disruption.
The four constraints — LR target, volume floor, ENBP, factor bounds — capture every material dimension of the pricing decision. The efficient frontier and shadow prices translate the mathematical output into the language of a pricing committee conversation. The compliance checks (ENBP per-policy, convergence verification) provide the FCA audit trail.
The stochastic extension, the cross-subsidy analysis, and the limitations section provide the honest accounting that actuarial sign-off requires. The solution from this module is not "the answer" — it is one principled input to a pricing committee decision that also involves competitive intelligence, underwriting judgment, and commercial priorities. The optimiser's contribution is to make the technical trade-offs visible and quantified, so the committee can focus on the decisions that genuinely require judgment.