Mathematics, Stochastic Modelling, Quantitative Finance, Finance, Probability.
respect to 𝑊t² : 3. Itô’s Lemma for a function 𝑦(𝑡,𝑊𝑡) is: Since 𝑦 does not explicitly depend on 𝑡t, the partial derivative with respect to 𝑡 is zero: ∂𝑦/∂𝑡=0; we substitute into ito’s lemma we obtain : Recall that 𝑦 = exp⁡(𝑊𝑡) Since 𝑦=𝑓, we can rewrite the differential equation in the form 𝑑𝑓​: