Geometric Brownian Motion — Explicit Solution

Easy

Exercise 1 / 3

Answer

Let $(W_t)_{t \geq 0}$ be a standard Brownian motion, and let $S_t$ be a process satisfying the following stochastic differential equation:

dS_t = \mu S_t \, dt + \sigma S_t \, dW_t, \quad S_0 > 0.

Question: Find an explicit expression for $S_t$ .

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S0

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0.