In Pay-As-You-Drive (PAYD) automobile insurance, the premium is fixed based on the distance traveled, while in usage-based insurance (UBI) the driving patterns of the policyholder are also considered. In those schemes, drivers who drive more pay a higher premium compared to those with the same...

The "hunger for bonus" is a well-known phenomenon in insurance, meaning that the insured does not report all of his accidents to save bonus on his next year's premium. In this article, we assume that the number of accidents is based on a Poisson distribution but that the number of claims is...