Can You Solve This Quant Interview Question? — The Time Integral of Brownian Motion

In this video we solve a real Quant Interview question involving the time integral of Brownian motion. While it frequently appears in quant interviews, its technical nature also makes it a classic exercise in stochastic calculus courses. We break it down step-by-step, so whether you're preparing for interviews, reviewing stochastic calculus, or just curious about Brownian motion, you'll find this problem both interesting and instructive. ⏱️ Timestamps 0:00 Intro 0:18 Problem statement 0:47 Martingale definition 1:57 Brownian motion review 3:18 Time Integral of BM 4:24 Fubini's Theorem 5:55 Expected value of X_t 7:20 Variance of X_t 8:46 Is X_t a martingale? 10:22 Outro --- If you enjoyed the video, please leave a like, subscribe, and let me know in the comments what topics or problems you’d like to see next! #quant #brownianmotion #finance #interview #maths