Black-Scholes Derivation — Delta Hedging Argument

source: https://thefinancialengineer.org/financial-engineering/volatility-engineering-and-volatility-trading/

In order to derive the Black Scholes PDE from the Brownian Motion using the Delta-Hedging Argument, we have to set up our self-financing portfolio first. This portfolio will be comprised of an option, ∆ units of the underlying stock, and a bank account, B. The goal is to make our portfolio risk-free, i.e. insensitive to changes in the price of the security.