Expectations vs. Arbitrage Pricing (Baxter & Rennie): I

I am told that Baxter and Rennie (BR; Financial Calculus) warns against always starting out with Expectations based pricing by arguing that it assumes the strong law of large numbers to hold - in essence, a statistically motivated argument.

I haven't seen where BR says that (so may be I shouldn't even talking about it), but that to me is quite wrong motivation for favouring no-arbitrage based pricing over expectations based pricing. Expectations based pricing works under the risk-neutral measure, or alternatively, assuming that agents making investment decisions are risk neutral. The reason why it works isn't based on the statistical properties of the stock price process.

Theoretically, of course, the mathematical equivalence between no-arbitrage and existence of a risk-neutral measure always holds. In practice, favouring one over the other would depend on the problem. So, it was rather surprising to come across a statisitcally motivated argument. Since it's claimed to be coming from a source like BR, it's likely I am interpreting it wrongly. Should check it out on my own.