David, sorry to hear of your bad university experience. I expect the industry was more appreciative.
I am trying to work my way more carefully through the Ross Recovery literature: Ross, Carr & Yu, etc. While Ross Recovery is a very novel insight, my read so far is that the method requires, among other things, for stock prices to either:
(i) form (or be a component of) an (irreducible) finite-state Markov chain, or
(ii) (if lying in a continuous or unbounded discrete state space), to be "recurrent" .
(A sufficient, but not necessary, condition for recurrence is having a stationary distribution).
In my mind, this key recurrence requirement seems to preclude any stock price dynamics with long-run (mean) exponential growth -- including of course, special cases like GBM (Black-Scholes), GARCH, etc. Ross himself, in his J. Finance article, showed recovery didn't work under GBM, as the risk-aversion parameter (under that evolution) cannot be recovered from option prices alone.
Q1. Do I have this right?
Q2. If so, is insisting on "recurrent" stock prices not a deal-breaker in financial modelling? (i.e., any plausible dynamical model will have (trend) exponential growth of prices?)