January 8th, 2023, 5:03 pm
I looked briefly and also tracked down one of your references: Liu and Longstaff (2004).
Similarly to your paper, Liu and Longstaff introduce an asset process that admits an arbitrage under certain perfect market conditions. Then, they were able to show that with a fairly minimal addition of realism (margin collateral), the putative asset process could 'persist' in the market, at least for log-utility investors, as there would not be an infinite demand for the arb strategy.
Anyway, my comment is that it might be interesting to raise a similar question with your reflecting process. That is, is there a fairly minimal addition of realism that would allow the process to persist without infinite demand for the stock as the barrier was about to be hit?
My thought is that perhaps this would require the interest rate to become stochastic and go to +infinity (briefly) on a barrier hit. The rationale would be that the interest rate would be paid by the govt intervener to keep the asset price above the barrier. If so, (i) would this translate to a finite or infinite dollar cost to the govt over a horizon T? and (ii) would it then also prevent an infinite demand for the stock -- as a riskless bond would become locally more attractive?
If the barrier were an upper reflecting barrier, perhaps the borrow cost of the stock would (briefly) go to +infinity. Something like that seems to be going on with the AMC/APE (pseudo-) arbitrage, which is of current interest. This is q (rather than r) -> +infinity, as the (institutional) holder of the stock will reap the borrow cost.