Dynamics of bankrupt stocks

We model and study the behavior of bankrupt stocks. We are interested in the dynamics of stocks and options, and in particular the cost of establishing positions with negative delta. This extends a model of Avellaneda and Lipkin which was used to model hard-to-borrow stocks. This model is a two-dimensional integrate-and-fire model which captures the self-reinforcing aspect of short squeezes and subsequent "crashes" when price support at some point vanishes. The only source of randomness in our model is the timing of these crashes. We understand the asymptotic behavior of this model and the risk-neutral measure.