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.