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Medium · Finance · Quant Trader interview question · stochastic-calculus, gbm, expected-value, probability
Suppose a stock price, $S_t$, follows a Geometric Brownian Motion (GBM) process defined by the stochastic differential equation: $dS_t = \mu S_t dt + \sigma S_t dW_t$ where: $\mu$ is the constant drift (expected rate of return). $\sigma$ is the constant volatility. $dW_t$ is a Wiener process (Brownian motion). Given an initial stock price $S_0$ at time 0, what is the expected stock price at time $t$, i.e., what is $ES_t$?