IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov chains
A two-state Markov chain on {A,B} has P(A→B)=0.2 and P(B→A)=0.3. What is its stationary distribution (π_A, π_B)?
The stationary distribution is (0.6, 0.4). Balance between the two states requires 0.2π_A = 0.3π_B, giving a ratio of 3 to 2, which normalises to 0.6 for A and 0.4 for B.
- A(0.4, 0.6)
- B(0.5, 0.5)
- C(0.6, 0.4)Correct
- D(0.7, 0.3)
- (0.2, 0.3)
Explanation
Balance requires π_A×0.2 = π_B×0.3, so π_A/π_B = 3/2. With the sum equal to 1, π_A=0.6 and π_B=0.4. The option (0.4,0.6) reverses the ratio.
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