Double Ncd System Pricing And Deductibles Optimal Settings

The determination of premiums is very important to the insurance company whether from the considerations of the perspective of the insurance company earnings or from the probability of ruin. Now, the NCD system and the deductible have become more and more popular.This paper first discusses the pricing of a NCD system with two-layer discount, in which the insured receives a discount (d) in the absence of claims for k years, and will receive the discount (d) again if there is no claim for the next k years. We use Markov decision processes to give optimal decisions for both the insured and the insurer. The insured's optimal behavior is described by a set of damage threshold values, below which claiming is not worthwhile. And the insurer fixes a premium (c) and a discount (d), accounting for the reaction of the insured.Then, we discuss the optimal deductible design when we use the exponential utility function. We study whether there exist a optimal deductible to make the utility function of the insurance company's profit become maximum. We discuss two situations. One is the absolute deductible, the other is the relative deductible.