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Exponential Martingale Expectation

Hard · Stochastic Calculus · Quant Trader interview question · stochastic calculus, martingale, brownian motion, expectation

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 $EM_t$?