Why Joshi defined option value to be discounted payoff using risk neutral expectation?

Question

Currently I am reading Mark Joshi's The Concepts and Practice of Mathematical Finance.

At page $59,$ the author mentioned the following.

Instead of requiring that every portfolio should have expectation equal to today's value, we require that its expectation should be equal to the asset's value invested at the risk-free growth rate, or equivalently that its discounted expectation is equal to today's value. We thus want $$\mathbb{E}_{RN}\left( \frac{A_{\Delta T}}{B_{\Delta T}} \right) = \left( \frac{A_0}{B_0} \right)$$ for every asset where $$\mathbb{E}_{RN}$$ is an expectation with the risk-neutral probability $p$.

This equation is trivially satisfied for the bond and we have the chosen the risk-neutral probability so that it is satisfied by construction for the stock. This leaves us with the option we wish to price. We define Opt$_0$ to satisfy equation above: $$Opt_0 = \mathbb{E}_{RN}\left( \frac{A_{\Delta T}}{B_{\Delta T}} \right) = e^{-r\Delta t} \mathbb{E}_{RN}(f(S))$$ where $f$ is the option's payoff.

My question is the following:

Question: Why and how can Joshi define option value at time zero to be the discounted risk neutral expectation?

Answer 1

Most of the Options pricing literature (except dynamic programming and reinforcement learning) is based on the assumption that options themselves are redundant. They can be artificially recreated with stocks and cash, hence options themselves carry no risk and every price is computed as "fair price" in a risk neutral fashion, needless to say options mostly don't trade at fair prices.