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Ornstein-Uhlenbeck

Assume a stock price process $S_t$ is governed by the stochastic differential equation $$dS_t = \alpha \left( \mu - S_t \right) dt + S_t \sigma dW_t,$$ with $\alpha$, $\sigma$ and $\mu > 0$. What qualitative behaviour does the process have, and what is the impact of the parameters $\alpha$ and $\mu$?

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  • Difficulty: Medium
  • Topic: Mathematics
  • Solution:
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