# If the risk neutral probability measure and the real probability measure should coincide

Sorry if this may be a stupid question. I have not had that much mathematical finance, I've only learned about discrete time models.

But lets for the argument say that you have a stochastic process of risky assets a bank process and a given probability measure for the market.

Then you calculate the risk neutral probability measure, and let's just assume that you get an unique measure that happen to coincide with the probaiblity measure for the market.

Is this then some kind of special stock market? When the probability measure and the risk neutral probability measure happen to be the same? Will it behave differently than other markets? Are they unrealistic?

The only difference I can think of is that the pricing will be done in a way a statistician would price it, since the pricing will follow the expected value under the normal probability measure also. But will something else happen? And if these markets are unrealistic, why are they that?, what would disrupt them?

A classic experiment to distinguish between risk-taking appetites involves an investor faced with a choice between receiving, say, either \$\$$100 with 100% certainty, or a 50% chance of getting \$$200. A risk-neutral agent is indifferent.