Pricing NCD System with Different Discount Levels

We price a NCD system with different discount levels, in which the insured receives the discount levels d_i when he/she has no claims for _i years. The NCD system can encourage the insured to keep cautious against risks, and save a lot of small account claims expenses for the insurers. The paper gives optimal decisions for both the insured and the insurer. For the insured, whether to claim depends on whether the realized damage exceeds the threshold values, given the offered contract, and the number of years without claims. In addition, the insurer should decide how to design optimal discount levels when he considers the insured’s reaction.