Experience Rating: Advanced Credibility and NCD Systems

No-Claims Discount Systems

No-claims discount (NCD) or bonus-malus systems adjust premiums based on claim history. The system is modeled as a Markov chain where states represent discount levels. Transition rules define how claims and claim-free years change the level. The stationary distribution gives long-run proportions at each level. The relativity at each level determines the premium charged. Optimal NCD systems (Bayesian) set the premium at each level equal to the expected claim frequency given the claim history implied by that level, using Bayesian updating. The efficiency of an NCD system measures how well it separates good from bad risks.

Advanced Credibility in Experience Rating

Beyond standard Buhlmann credibility, advanced methods allow for correlation between past observations (serial correlation credibility), trends in experience, and multiple risk characteristics. The credibility regression model (Hachemeister) allows relativities to vary by risk class with credibility-weighted estimates. Bayesian updating for bonus-malus uses conjugate models: Poisson frequency with Gamma prior gives a closed-form posterior. The predictive premium for a policyholder with k claims in n years of exposure is (alpha + k)/(beta + n) times the base premium. Exam MAS-II tests NCD Markov analysis and advanced credibility applications.