The Economic Plausibility Of Strict Local Martingales In Financial Modelling

The context for this paper is a continuous financial market consisting of a risk-free savings account and a single non-dividend-paying risky security. The authors present two concrete models for this market, in which strict local martingales play decisive roles. The first admits an equivalent risk-neutral probability measure under which the discounted price of the risky security is a strict local martingale, while the second model does not even admit an equivalent risk-neutral probability measure, since the putative density process for such a measure is itself a strict local martingale.