Pricing no claims discount systems

We price a no claims discount (NCD) system, in which the insured receives a discount (d) in the absence of claims for k years. The paper gives optimal decisions for both the insured and the insurer, using Markov decision processes and game theory. The company fixes a premium (π) and a discount (d), accounting for the reaction of the insured. The insured decides whether to claim, given the offered contract, the realized damage level, and the number of years without claims. The insured's optimal behavior is described by a set of damage threshold values, below which claiming is not worthwhile.