In the online classroom the tutors keep mentioning that you can use Taylor's series instead of Ito's Lemma when asked to specifically use Ito Lemma in a question. Please can I clarify it is OK to use Taylor's series even if the question explicitly mentions Ito's Lemma? I don't recall the mark scheme providing the Taylor's series in their solutions, and so don't want to lose marks by using it if im not allowed to. Thanks, Min
Ito’s lemma is like the first few terms of a Taylor series. It can be informally derived by taking the Taylor expansion of the function up to its second derivatives and retaining the time terms up to first order the stochastic terms up to second order. I assume this is what the tutors are getting at. It’s a handy way of remembering Ito if you forget it, or of doing an informal derivation if the exam allows that.
The situation is entirely analogous to being asked to solve a quadratic by using THE quadratic formula (an ill defined question in itself if we really stop and think about it) and just deciding to instead complete the square. You can't be marked as not having done what is asked because THE quadratic formula comes from completing the square - you cannot complete the square without, in effect, using THE quadratic formula. Similarly, you cannot use Taylor's formula to derive an SDE without effectively using Ito's lemma as you do so. John
