For the needs of pricing it is important to know whether the discounted price process of an asset has the true martingale (not only local martingale) property. This is related to the absence of bubbles, etc. (to be discussed in the talk). We provide a criterion for the martingale property of the diffusions dX_t=\sigma(X_t)dB_t, which include in particular the CEV model.

Joint work with Peter Carr and Mikhail Urusov.