This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine the “default term” apparent in risk-neutral option prices if the underlying stock exhibits a bubble modeled by a strict local martingale. Results for certain path dependent options and last passage time formulas are given.
"Strict local martingales and bubbles." Ann. Appl. Probab. 25 (4) 1827 - 1867, August 2015. https://doi.org/10.1214/14-AAP1037