As you know, the _key equation_ of risk neutral pricing is the following:

$\exp^{-rt} S_t = E_Q[\exp^{-rT} S_T | \mathcal{F}_t]$

That is, discounted prices are Q-martingales.

It makes real-sense for me from an economic point of view, but is there any "proof" of that?

I'm not sure my question make real sense, and an answer could be "there is no need to prove anything, we create the RN measure such that this property holds"...

**UPDATE**: I'm looking to find a "justification" I could use to justify the equation above.

According to @Brian B, I should be able to say that if the market has no arbitrage, then it holds.

Using the first Fundamental Asset Pricing Theorem: _if a market model has a risk-neutral probability measure, then it does not admit arbitrage_

and the Second Fundamental Asset Pricing Theorem: _assuming a market model having a risk-neutral measure, then the model is complete iff the risk neutral measure is unique_,

I can't see how, even with a complete and arbitrage free-model, I can assure that Q exists.

Indeed, the second theorem depends on the first. Since the first theorem says "Q exists => there are no arbitrage", I can say that "if there is arbitrage, then Q does not exists" but since it's not an "iif" I can't say the reciprocal "if Q exists, then there is no arbitrage"... What am I missing?

I took the theorem definition from [Shreve 2004][1]


  [1]: http://www.amazon.com/Stochastic-Calculus-Finance-II-Continuous-Time/dp/0387401016/ref=sr_1_1?ie=UTF8&qid=1302814778&sr=8-1