Find the explicit solutions of the following stochastic differential equations: (a) Ornstein-Uhlenbeck process: [d X_{t}=mu X_{t} d

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Find the explicit solutions of the following stochastic differential equations:

(a) Ornstein-Uhlenbeck process:

\[d X_{t}=\mu X_{t} d t+\sigma d B_{t}\]

(b) Mean reverting Ornstein-Uhlenbeck process:

\[d X_{t}=\alpha\left(m-X_{t}\right) d t+\sigma d B_{t}\]

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Quantitative Finance

ISBN: 9781118629956

1st Edition

Authors: Maria Cristina Mariani, Ionut Florescu

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Question Posted: Apr 20, 2024 01:00 AM

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Find the explicit solutions of the following stochastic differential equations: (a) Ornstein-Uhlenbeck process: [d X_{t}=mu X_{t} d

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Quantitative Finance

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