Exam MAS-I Practice Question 18
Study guide: Exam MAS-I
A bonus-malus system has levels 1 to 5. Each year a policyholder moves up one level after a year with a claim, or down one level after a claim-free year, staying put at the ends. The level forms an ergodic Markov chain with stationary distribution \pi.
Which equation holds for every pair of adjacent levels i and i + 1, and why?
- A)
\pi_i P_{i,i+1} = \pi_{i+1} P_{i+1,i}, since up-crossings and down-crossings of that boundary alternate - B)
P_{i,i+1} = P_{i+1,i}, since a time-reversible chain must have a symmetric transition matrix - C)
\pi_i = \pi_{i+1}, since in the long run the chain spends equal time at every level - D)
\pi_i P_{i+1,i} = \pi_{i+1} P_{i,i+1}, since each flow is weighted by the probability of its destination - E)
\pi_i P_{i,i+1} = \pi_{i+1} P_{i,i+1}, since moving up and moving down are equally likely
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