IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
A symmetric simple random walk starts at 2 with absorbing barriers at 0 and 5. What is the probability it is absorbed at 5?
The probability is 0.4. For a symmetric walk, the chance of reaching the upper barrier first equals the starting position divided by the barrier distance, 2 over 5, since the walk is a martingale.
- A0.2
- B0.3
- C0.4Correct
- D0.5
- 0.6
Explanation
For a symmetric walk the gambler's ruin probability of hitting the upper barrier is start/upper = 2/5 = 0.4. The value 0.6 is the probability of ruin at 0, which is the complement.
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