1.

Determine the percentage of the basic premium to be paid by a Dutch driver, who originally entered the bonus-malus scale at level 100%, drove without claim for 7 years, then filed one claim during the eighth policy year, and has been driving claim-free for the three years since then. Would the total of the premiums he paid have been different if his one claim occurred in the second policy year?

1.

45%; 760% vs. 900%

1.

Prove (6.8).

2.

Determine P ² with P as in (6.1). What is the meaning of its elements? Can you see directly from this that l(2) = l( ?) must hold?

3.

Determine e( ?) in the example with three steps in this section if in state 2, instead of c the premium is a. Argue that the system can now be described by only two states, and determine P and l( ?).

4.

Show that e( ?) < 1 in (6.9) for every a and c with a < c. When is e( ?) close to 1?

5.

Recalculate (6.11) for a claim at the end of the policy year when the interest is i.

6.

[ ?] Calculate the Loimaranta efficiency (6.9) by method (6.17) (6.19).

7.

Determine the value of ? such that the transition probability matrix P has vector