Driving with Markov-programming

Let us consider tile following problem. A motorist has decided to effect an accident insurance under the following conditions. The insurance runs for one year. The premium for the first year amounts Eo. If no damages have been claimed during i successive years, i = z, 2 or 3 the premium is reduced to E~. After four years of damage free driving no further premium reduction is granted, so the premium remains Ea. The premium is due on the first day of the year t). The own risk amounts ao.