Exponential Martingale Expectation - Quant Trader Interview Question
Difficulty: Hard
Category: Stochastic Calculus
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Topics: stochastic calculus, martingale, brownian motion, expectation
Problem Description
Let $W_t$ be a standard Brownian motion. Define a stochastic process $M_t$ as:
$M_t = \exp(\theta W_t - \frac{1}{2}\theta^2 t)$
where $\theta$ is a constant. Assuming $M_t$ is a martingale with respect to the filtration generated by $W_t$, what is the value of $EM_t$?
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