The moment problem asks whether or not a given probability distribution is uniquely determined by its moments. The existence of moment-indeterminate distributions has been known since the late 19th century; however, first examples were often considered as mere mathematical curiosities. Recent research has shown that the problem is more widespread than previously thought and also that it is relevant in more practical contexts. Specifically, distributions that are not determined by their moments arise in applied economics, notably the modelling of economic size distributions, and also in mathematical finance. The project investigates determinacy issues for selected distributions from these fields.  It will also consider the multivariate case, for which current knowledge is much more fragmentary than in the classical univariate setting.