Quant Interview Recursion Guide
How to use recursion and state equations for quant interview probability, expected value, random walk, and stopping-time questions.
Candidates struggling with random walks, waiting times, stopping rules, and recursive probability prompts.
Define the state
Recursion starts with a state that contains all information needed to continue. For a random walk, the state may be position. For a coin pattern, the state may be current matched prefix. A vague state creates vague equations.
Write boundary conditions
Boundaries anchor the recursion. If a walk has absorbing barriers, write the value at each barrier before solving. If a game has a stopping payoff, write the payoff at the stopping state.
Separate probability and expectation
Hitting probability recurrences average neighboring probabilities. Expected time recurrences usually add one step before averaging future states. Mixing these two forms is a common interview mistake.
Concrete example
For a fair random walk from 1 with barriers at 0 and 3, let p_i be the chance of hitting 3 first. Then p_0 = 0, p_3 = 1, and p_i = 0.5p_{i-1} + 0.5p_{i+1}. Solving gives p_1 = 1/3.
Use recursion selectively
Recursion is useful when the future resembles the original problem after one step. If a direct complement or linearity argument solves the problem, use the simpler method. Recursion is a tool, not a badge of difficulty.
Common mistakes
Candidates skip boundary conditions, define states that omit important history, or add the extra step to a probability recurrence. Write states and boundaries before moving symbols around.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.