Underwriting, risk classification, experience rating, bonus-malus scales

In insurance, the pricing of risk is based on occurrence probabilities/frequencies and on loss severities. Actuarial pricing is used to develop technical premiums that are intended to cover losses from underwritten risks and provide future benefits payable to beneficiaries with a sufficiently high degree of confidence. These technical premiums form the starting point to determine the commercial ones, actually charged to policyholders and including shareholders’ profit. Contrary to technical premiums, which should be as accurate as possible, the commercial price list is often simplified. It is sometimes heavily regulated and also depends on market pressure.

In P&C, the pricing includes the design of appropriate experience rating schemes, updating future technical and commercial premium amounts based on past experience using credibility mechanisms or bonus-malus systems for instance. In Life & Health also, risk classification helps sponsors to better monitor their portfolios.

Actuarial valuation consists in estimating the future liabilities associated with past risk transfers. Valuation is required by regulators not just for insurance companies but also for self-insured operations. It can be useful in case of risk transfer or securitization.


What Detralytics can do for you

Detralytics actuaries have developed a unique expertise in actuarial pricing and valuation for both new and existing businesses. They master the related actuarial techniques, as well as innovative approaches inherited from biostatistics and data science. They can also propose a range of technical solutions to restore profitability, if needed.

Detralytics actuaries have accumulated deep knowledge in biometric risks (life tables, morbidity rates, etc.) and can assist your teams in the prospective study of your own portfolio experience. They specialize in the projection of future cash flows of existing portfolios, in both life and nonlife business.

Besides pricing, Detralytics can also assist you in the design of appropriate underwriting rules and to evaluate the need for solvency capital and reinsurance, including the corresponding costs into the resulting premiums. Detralytics can also help you to develop tools to assess intermediaries’ value (brokers or agents) so that commissions or discount capabilities can be adequately monitored.


Detralytics’ experience

Detralytics actuaries have assisted major European insurers to develop innovative a priori and a posteriori risk classification schemes in the main branches of P&C (motor, homeowner, general liability, workers’ compensation, etc.) as well as Life & Health. They have also worked in collaboration with some of the largest European reinsurers to develop innovative pricing tools.

Here are some examples of past projects related to actuarial pricing run by our actuaries:

  • Construction of a new technical price list for a major insurance company operating in Belgium, for workers’ compensation insurance.
  • Revision of the technical price list for several medium size insurance companies operating in Belgium and Luxemburg, for motor insurance.
  • Spatial modelling of risk in motor insurance for a major French mutual insurance company.
  • Development of an actuarial model assessing the profitability of intermediaries in motor insurance.
  • Evaluation of the assessment grid used in homeowner insurance by an insurer operating in Belgium.
  • Revision of the technical price list for a leading Belgian mutual insurance company in complementary health insurance (hospital and dental coverage) and projections of the increases in claim costs.
  • Risk classification in life insurance and lapse rate modelling for a major German reinsurer.
  • Development of relational and credibility models in life insurance for a major French reinsurer.
  • Projections of the costs of pension for civil servants, performed for the Belgian Ministry of Finance.
  • Creation of the medical index and the medical liability fund under the Belgian law.
  • Development of a Farm Income Stabilisation Tool for the Wallonia Region.
  • Development of the loss distribution approach to operational risk in line with the Basel Committee proposal for the world largest settlement bank.


Our senior actuaries also act as experts for Belgian courts, in trials involving technical insurance matters.

Detralytics actuaries co-authored reference texts on actuarial pricing, sometimes written in collaboration with members of the actuarial teams working for partners (re)insurers. Here is a short selection of the methodological contributions by our senior actuaries, including the following books:


  • Denuit, M., Maréchal, X., Pitrebois, S., Walhin, J.-F. (2007). Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems. Wiley, New York.
  • Pitacco, E., Denuit, M., Haberman, S., Olivieri, A. (2009). Modelling Longevity Dynamics for Pensions and Annuity Business. Oxford University Press.
  • Denuit, M., Robert, C. (2007). Actuariat des Assurances de Personnes: Modélisation, Tarification et Provisionnement. Collection Audit-Actuariat-Assurance, Economica, Paris.
  • Denuit, M., Charpentier, A. (2005). Mathématiques de l’Assurance Non-Vie. Tome II: Tarification et Provisionnement. Collection Economie et Statistique Avancées, Economica, Paris.

Scientific papers

And some scientific papers published in the last few years:

  • Dhaene, J., Godecharle, E., Antonio, K., Denuit, M., Hanbali, H. (2017). Lifelong health insurance covers with surrender value: Updating mechanisms in the presence of medical inflation. ASTIN Bulletin.
  • Gbari, S., Poulain, M. Dal, L., Denuit, M. (2017). Extreme value analysis of mortality at the oldest ages: A case study based on individual ages at death. North American Actuarial Journal.
  • Denuit, M., Dhaene, J., Hanbali, H., Lucas, N., Trufin, J. (2017). Updating mechanism for lifelong insurance contracts subjec to to medical inflation. European Actuarial Journal.
  • Denuit, M., Trufin, J. (2016). From regulatory life tables to stochastic mortality projections: The exponential decline model. Insurance: Mathematics and Economics 71, 295-303.
  • Schinzinger, E., Denuit, M., Christiansen, M. (2016). A multivariate evolutionary credibility model for mortality improvement rates. Insurance: Mathematics and Economics 69, 70-81.
  • Cadena, M., Denuit, M. (2016). Semi-parametric accelerated hazard relational models with applications to mortality projections. Insurance: Mathematics and Economics 68, 1-16.
  • Gbari, S., Denuit, M. (2015). Stochastic approximations in CBD mortality projection models. Journal of Computational and Applied Mathematics 296, 102-115.
  • Denuit, M., Trufin, J. (2015). Model points and Tail-VaR in life insurance. Insurance: Mathematics and Economics 64, 268-272.
  • Denuit, M., Haberman, S., Renshaw, A. (2015). Longevity-contingent deferred life annuities. Journal of Pension Economics and Finance 14, 315-327.
  • Pigeon, M., Henry de Frahan, B., Denuit, M. (2014). Evaluation of the EU proposed Farm Income Stabilisation Tool by Skew Normal Linear Mixed Models. European Actuarial Journal 4, 383-409.
  • Gbari, S., Denuit, M. (2014). Efficient approximations for numbers of survivors in the Lee-Carter model. Insurance: Mathematics and Economics 59, 71-77.
  • Klein, N., Denuit, M., Lang, S., Kneib, Th. (2014). Nonlife ratemaking and risk management with Bayesian additive models for location, scale and shape. Insurance: Mathematics and Economics 55, 225-249.
  • Gschlossl, S., Schoenmaekers, P., Denuit, M. (2011). Risk classification in life insurance: Methodology and case study. European Actuarial Journal 1, 23-41.
  • Delwarde, A., Kachakhidze, D., Olié, L., Denuit, M. (2004). Modèles linéaires et additifs généralisés, maximum de vraisemblance local et méthodes relationnelles en assurance sur la vie. Bulletin Français d’Actuariat 6, 77-102.


Given their recognised expertise, our senior actuaries often act as trainers on actuarial pricing and valuation topics. Here are some examples of Detralytics’ offer in terms of training:

  • Risk classification in nonlife insurance with GLM regressions and their extensions, GAM, GAMLSS, Regularizations (Lasso, Ridge, Elastic net, …), Gradient Boosting, Random Forests, etc.

Such topics have been presented at International Summer School of the Swiss Association of Actuaries, Warsaw Actuarial Summer School, ASTIN Seminar in Actuarial Mathematics, CPD sessions for Munich Re, the Swiss Association of Actuaries, Caritat, or IABE, for instance.

  • Quantification of Life & Health mortality, longevity and morbidity risks.

Such topics have been presented at Summer School of the Groupe Consultatif actuariel européen, Forum suisse de la prévoyance professionnelle, Warsaw Actuarial Summer School, CPD sessions for IABE, or ILAC, for instance.