Martingales for Interview Problems

Martingales for Interview Problems#

Most candidates who get a gambler's ruin problem at Jane Street or Citadel reach for recursion. They write out $p(k) = \frac{1}{2}p(k+1) + \frac{1}{2}p(k-1)$, solve the characteristic equation, apply boundary conditions, and spend five minutes on algebra that a martingale argument finishes in thirty seconds. Interviewers notice. The recursion isn't wrong, but it signals that you're computing your way through a ...