We solve the problem of valuing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Karatzas and Fernholz (Handbook of Numerical Analysis, vol. 15, pp. 89–167, Elsevier,...

We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are them- selves local martingale deflators...