IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov chains
A No Claims Discount system for an Indian motor insurer has discount levels 0%, 20% and 40% (states 1, 2, 3). The annual probability of at least one claim is 0.25. After a claim-free year the policyholder moves up one level (staying at 40% at the top); after a year with a claim they move down one level (staying at 0% at the bottom). A policyholder starts at 20%. What is the probability of being at 40% after two years?
The probability is 0.5625. To be at the top level after two years, the policyholder must be claim-free in both years, starting from the middle level, which has probability 0.75 squared. A claim in the first year would leave them too low to reach the top.
- A0.5625Correct
- B0.1875
- C0.7500
- D0.0625
- 0.4375
Explanation
Start at state 2. After year 1: state 3 with 0.75, state 1 with 0.25. After year 2: from state 3, stay at 3 with 0.75, giving 0.75*0.75 = 0.5625. From state 1, only reaching state 2 is possible, not 3. So the probability is 0.5625. The value 0.75 ignores the second year.
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