If the goal is a discrete version of Black-Scholes, this seems backwards to me. The standard discrete description of dynamic hedging using discrete steps for time and price on a binomial tree (you can easily extend it to a recombining multinomial tree, too) is for me the best discrete version of Black-Scholes. In particular, this description makes it quite clear why you want to use pseudo-probabilities and not real probabilities.

The continuous version of Black-Scholes is easily derived from this by taking a limit.

I guess I'm a Luddite, but I've never understood the need to know Ito's lemma and stochastic calculus when doing mathematical finance. The real world is discrete. Simple continuous limits such as Black-Scholes are extremely useful, but I've never fully understood why anyone would want to use overly sophisticated continuous stochastic models. The real world is far too noisy.