GBM Expected Value - Quant Trader Interview Question
Difficulty: Medium
Category: Finance
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Topics: stochastic-calculus, gbm, expected-value, probability
Problem Description
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 $ES_t$?
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