Drunk on Returns

What this random-walk barrier problem tests

This is an easy probability question testing your ability to reason about absorbing barriers in a symmetric random walk. It's the kind of problem quant trading desks use to see whether you can set up and solve a classic martingale or gambler's-ruin scenario quickly and cleanly.

To solve it, you'll need to model the process as a discrete random walk on the integers, identify the two absorbing states (the "ruin" and "profit" boundaries), and then apply either a recursive argument or a closed-form formula for the probability of reaching one barrier before the other. The symmetry of the problem and the specific starting position are both important.

• Absorbing barriers and stopping times
• Martingale approach vs. difference-equation approach
• Boundary conditions and recursive setup