Itô's Lemma: What Does It Teach Us

What does Itô's Lemma teach us and what are some uses?

Answer

Itô’s Lemma tells us how to differentiate functions of stochastic processes (a stochastic chain rule).

Some practical uses are the following (list is very, very basic):

  • Solving SDEs (e.g., Geometric Brownian Motion).

  • Showing martingality (e.g., $B_t^2 - t$).

  • Computing expectation/variance of complex stochastic processes.

Back to collection