A Numerical Method of Finding a Suitable Bonus Scale

The bonus system used by Finnish insurers is as follows: Policies are divided into 4 bonus classes, C1, C2, C8, C4, each of them being initially placed in class C 1. After one clairnless year, a policy placed in class Ch is transferred to class C h ÷ 1 (h _ 3) from the beginning of the following year. After a claim year, each policy is entered back to class Cv (Whether the number of claims is one or more does not play any role in this transition system.)