Fourier series

October 15, 2023

fourier series #

watching fourier transforms #

https://www.youtube.com/playlist?list=PLB24BC7956EE040CD

Following is a summary of lecture 1 - 4. #

https://chat.openai.com/share/9f767d73-175a-4f1b-b476-7c1f10988e66

heat equation #

comes up as the application of fourier series

https://chat.openai.com/share/a66f3b58-13d9-4273-8713-057d72e1e527

I had a slightly miguided impression on the “periodic nature” of the problem where the object’s shape is a ring. In the end, the discussion due to the misinterpretation led me to understand what to expect from “Fourier transform” (opposed to fourier series)

Black-Scholes equation #

https://chat.openai.com/share/166b2c1c-670b-4ea8-a4ad-60e917d4ec1a

heat (defusion) equation uses idea of

• flow
• conservation

Where the discrepance between amount of energy flow-in and flow-out should be equal to the energy stored inside the region.

asked if there’s financial example of flow / conservation principle applied to finance, and GPT answered Black-Scholes

It seems the connection is rather weak here though, you only get to interpret the flow / conservation in the equation after you set up the modeling. Wheares in diffusion equation, the flow / conservation idea is used to setup the model.

put / call option #

What is put / call option

https://chat.openai.com/share/95bf4961-084e-4916-a195-059690ec5300

Does derivative inflate underlying asset price?