IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Stochastic processes
A simple random walk starts at 2 and moves +1 with probability 0.5 and -1 with probability 0.5 at each step. There are absorbing barriers at 0 and 5. What is the probability the walk is absorbed at 5 rather than 0?
For a symmetric walk with absorbing barriers at 0 and 5, the probability of reaching 5 first from 2 is 2/5 = 0.40, since the probability is proportional to the starting distance from the lower barrier.
- A0.20
- B0.60
- C0.50
- D0.40Correct
- 0.25
Explanation
For a symmetric walk the probability of hitting the upper barrier b before 0 starting from k is k/b. Here k = 2 and b = 5, giving 2/5 = 0.40. The value 0.60 is the probability of ruin at 0, and 0.50 wrongly applies symmetry of the steps to the position.
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