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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov chains

A no-claims-discount model has states 0%, 20% and 40%. Whether a policyholder moves depends only on the current level and whether a claim is made in the year. Why would the process of the discount level be a time-homogeneous Markov chain?

The discount level is a time-homogeneous Markov chain because the next level depends only on the current level and the year's claim outcome, and the claim probability is constant over time. A finite state space alone is not sufficient, and levels are not independent.

  1. ABecause claim probability is the same each year and the next level depends only on the current level and that year's claim outcomeCorrect
  2. BBecause the discount level can never decrease
  3. CBecause the discount level at each time is independent of the level at the previous time
  4. DBecause the state space is finite, so every process on it is Markov
  5. Because the premium depends on the full claim history over all years

Explanation

The next level is determined by the current level and a claim outcome whose probability does not change with time, giving the Markov property and constant transition probabilities. A finite state space alone does not guarantee Markov behaviour, and independence between successive levels would contradict the dependence in the model.

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