HardStochastic Processes
Reflection Principle for the Maximum
CitadelDE Shaw
For a standard Brownian motion on [0, 4], what is the probability that its running maximum exceeds 2? (Φ(1) ≈ 0.8413.)
Approach
Reflect the path at the first touch of level 2.
P(max ≥ a) = 2P(W_T ≥ a).
Answer
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