This paper studies a Stieltjes-type moment problem defined by the generalized
lognormal distribution, a heavy-tailed distribution with applications in
economics, finance and related fields. It arises as the distribution of the
exponential of a random variable following a generalized error distribution,
and hence figures prominently in the EGARCH model of asset price volatility.
Compared to the classical lognormal distribution it has an additional shape
parameter. It emerges that moment (in)determinacy depends on the value of this
parameter: for some values, the distribution does not have finite moments of
all orders, hence the moment problem is not of interest in these cases. For
other values, the distribution has moments of all orders, yet it is
moment-indeterminate. Finally, a limiting case is supported on a bounded
interval, and hence determined by its moments. For those generalized lognormal
distributions that are moment-indeterminate Stieltjes classes of
moment-equivalent distributions are presented.Comment: 12 pages, 1 figur
