“Awareness is learning to keep yourself company.” _ -- Geneen Roth_

This book reminds me of “Elementary Stochastic Calculus with Finance in view”, a book by Thomas Mikosch, in terms of the overall goal. This book has a goal of making the reader understand the nuts and bolts of Black Scholes pricing formula. Probability theory, Lebesgue integration and Ito Calculus are the main ingredients in the Black Scholes formula and these rely on set theory, analysis and an axiomatic approach to mathematics.

[Right from the preface of the book, Prof. David Williams emphasizes that intuition is more important than rigour. The definition of probability in terms of long term frequency is fatally flawed and hence the author makes it very clear in the preface that “probability works only if we do not define probability in the way we talk about probability in the real world”. Meaning colloquial references to probability gives rise to shaky foundations.

Solving an SDE analytically can be done only in few instances(toy SDEs). For the majority of the cases, one solves it numerically. Having said that, this book can be read by anyone who is interested in understanding SDEs better. Simulation is a great way to understand many aspects of Stochastic processes. For example, you can read through Girsanov theorem for change of measure, but by visualizing it through a few sample paths, you have a deeper understanding .