NYU and Morgan Stanley

The Ross Recovery Theorem gives sufficient conditions under which the

market’s beliefs

can be recovered from risk-neutral probabilities. His approach places

mild restrictions on the form of the preferences of

the representative investor. We present an alternative approach which

has no restrictions beyond preferring more to less,

Instead, we restrict the form and risk-neutral dynamics of John Long’s

numeraire portfolio. We also replace Ross’ finite state Markov chain

with a diffusion with bounded state space. Finally, we present some

preliminary results for diffusions on unbounded state space.

In particular, our version of Ross recovery allows market beliefs to be

recovered from risk neutral probabilities in the classical Cox

Ingersoll Ross model for the short interest rate.