Ensuring finite moments in Monte Carlo simulations via iterated ex post facto sampling

Monte Carlo simulations may involve skewed, heavy-tailed distributions. When variances of those distributions exist, statistically valid confidence intervals can be obtained using the central limit theorem, providing that the simulation is run ‘long enough.’ If variances do not exist, however, valid confidence intervals are difficult or impossible to obtain. The main result in this paper establishes that upon replacing ordinary Monte Carlo sampling of such heavy-tailed distributions with ex post facto sampling, estimates having finite moments of all orders are ensured for the most common class of infinite variance distributions. We conjecture that this phenomenon applies to all distributions (having finite means) when the ex post facto process is iterated.