Citadel Quant Research Intern Interview Questions
Are you preparing for a Citadel Quant Research Intern interview? Mastering classic probability puzzles such as the Gambler’s Ruin problem is essential for standing out in the highly competitive quant research recruitment process. This article offers a comprehensive, step-by-step explanation of the Gambler’s Ruin problem—one of the most frequently asked stochastic process questions in quant interviews. Here, we’ll break down the underlying concepts, solve for the probability of reaching a target wealth, and determine the expected duration until ruin or success, using both mathematical derivations and code examples.
The Gambler’s Ruin problem is a classical question in probability theory and stochastic processes. It models a scenario where a gambler repeatedly bets on a fair or unfair game, aiming to reach a target wealth before going broke. This problem is foundational in understanding random walks, Markov Chains, and is highly relevant in both financial mathematics and quantitative research interviews.
Imagine a gambler starts with \( i \) dollars and wants to reach \( N \) dollars. At each round, the gambler either wins one dollar with probability \( p \), or loses one dollar with probability \( q = 1 - p \). The game ends when the gambler either reaches \( 0 \) (ruin) or \( N \) (success).
