Actuarial and Quantitative Risk
The Global Risks Alliance (GRA)
Many risks have little data: new products, small portfolios, rare perils and emerging markets. Credibility theory blends a portfolio's own experience with wider data according to how much the own data can be trusted. Bayesian methods, pooling and expert judgement extend this. This page sets out how actuaries estimate risk with sparse data, where estimates go wrong, the sources used and who decides.
GRA · In development · service level R0
Credibility theory is the actuarial method of blending a portfolio's own experience with wider data according to how much the own data can be trusted. With Bayesian updating and structured expert judgement it supports estimates where data are sparse. Actuaries, product committees, supervisors and reinsurers hold the decisions.
How a dry season is read against the point where drought cover starts to pay. Synthetic season and design terms.
Working where loss history is short or missing. The dossier below sets out how the risk develops, what is measured, where the data come from, how it is modelled and who decides.
Credibility weights give more weight to own experience as it grows. Too little weight ignores real differences; too much prices on noise.
Industry or reinsurer benchmarks reflect other portfolios. If the portfolio differs in mix or practice, the blend carries bias.
Where data are absent, structured expert elicitation provides estimates. Without structure and documentation, judgement adds hidden bias.
Bayesian updating revises estimates as experience accumulates, showing how far data have moved the prior assumption.
Each term as this page uses it. Where a standard-setting body defines the term, the wording follows that body.
| Term | Definition |
|---|---|
| Credibility weight | The proportion of weight given to own experience when blending it with broader data. |
| Prior distribution | A probability distribution expressing beliefs about a parameter before new data are considered. |
| Expert elicitation | A structured process for obtaining and combining quantitative judgements from experts. |
Each indicator carries its unit, its cadence, the kind of source behind it and the evidence label a value would carry. No values are shown: a programme supplies them under its own authority.
| Indicator | Unit | Cadence | Source type | Label |
|---|---|---|---|---|
| Credibility weight assigned to own experience | proportion, zero to one | per analysis | Pricing analysis | MODELLED |
| Exposure underlying own experience | exposure units | per analysis | Portfolio data | OBSERVED |
| Difference between own and benchmark estimates | percent | per analysis | Pricing analysis | ESTIMATED |
| Expert elicitation sessions documented | count | per model | Model documentation | DECLARED |
| Posterior uncertainty of key parameters | interval width | per analysis | Bayesian models | MODELLED |
| Actual-to-expected ratio after launch | ratio | periodic | Experience monitoring | ESTIMATED |
The topic as a computational graph: named sources feed the methods, an evidence review gates the outputs, and the decisions stay with the authorities that hold them.
Fig. 02Nodes carry their type, two metric rows and a state; connectors show what feeds what; dashed frames name the owners; the timeline is the cadence. Design of the pipeline, not a record of a run.
Named public datasets and institutional records, each with its licence class. Sources by agreement are used only under their terms and never republished.
| Source | What it gives | Licence class |
|---|---|---|
| Actuarial Standards Board ASOP on credibility procedures | Professional standards for credibility | Free, ASB terms |
| Casualty Actuarial Society credibility monographs | Bühlmann and limited fluctuation methods | Free to read, CAS terms |
| Industry statistical agent data | Pooled experience for benchmarks | Licensed, terms per agent |
| Structured expert judgement literature (Cooke method) | Methods for eliciting and combining expert estimates | Free to read, terms per publisher |
| Stan and PyMC documentation | Open-source Bayesian modelling tools | Open source, BSD and Apache licences |
Actuarial and Quantitative Risk prepares evidence. The decisions below are taken by the authorities named, under their own rules, and never by the platform.
| Who decides | The question | Evidence this page serves |
|---|---|---|
| Pricing and reserving actuaries | How much credibility to give own data and which benchmark to use | Exposure, benchmark relevance and professional standards |
| Product committees | Whether to launch products with sparse data and what monitoring applies | Uncertainty estimates and monitoring plans |
| Supervisors | Whether assumptions for new or small portfolios are reasonable | Actuarial reports |
| Reinsurers | How to price cover for portfolios with little history | Benchmarks and exposure data |
Credibility theory, developed by actuaries over many decades, blends a risk's own experience with a broader collective estimate, giving more weight to own experience as its volume and stability grow. The Bühlmann and Bühlmann-Straub models formalize this as a linear estimate that minimizes expected error, and they are closely related to Bayesian methods and to hierarchical models in statistics.
Hierarchical Bayesian models extend the idea, letting groups such as regions, industries or policy types share information while retaining their own parameters. They make uncertainty explicit and can incorporate prior knowledge from expert judgement or related data. Structured expert elicitation methods help reduce bias when experts supply estimates.
In emerging risks such as cyber, the problem is not only volume but change: the threat environment evolves faster than data accumulate, so old data may be less relevant. In lower-income markets, using models built for other countries can embed assumptions about building quality, health or behaviour that do not hold.
Blending own and collective experience; requires a sensible definition of the collective.
Sharing information across groups with explicit uncertainty; results depend on priors.
Formal methods to obtain and calibrate expert judgement.
Limits: no method creates information that is not there. Sparse-data estimates carry wide uncertainty, and results can be dominated by assumptions about the collective or prior.
The current service level is R0: information and enquiries. An enquiry receives a reference and names the next step; applications, payments, compute allocations and registrations open only when their team, terms and review capacity exist.