Introduction

This web book is built around Malliavin Calculus and the Clark-Ocone formula. After many months of frustration, I figured the main obstacle with learning the topic is the emphasis on mathematical rigor over pedagogical clarity, so I hope to bridge that gap. I’m assuming just basic knowledge of algebra, analysis and probability.

I will start with developing what Malliavin calculus was meant to address. I will approach it in an indirect, meandering way. After documenting situations were a problem exists, the need for a solution will generate a “vacuum” of sorts. Following that, again indirectly, I’ll lay the foundation step by step. Finally, the vacuum will be filled.

As mentioned, pedagogical clarity is the guiding factor. I’ll disregard proofs if I don’t see them important. Shortcuts will be taken liberally. Some pieces will lead nowhere or be there just to round up a concept. I may even admit when I’m ignorant about something and leave it like that.

Truth is, I’m not a mathematician, a statistician or an economist. I’m just trying to understand an obscure topic.

Now, it’s time to start.

---