A colleague of mine posed a question to me regarding certain distributions used in loss models. Naturally occurring distributions, such as inverse Pareto, do not have finite moments. But naturally occurring questions within actuarial science, such as those involving expected shortfall, involve moments or moments of right tails. Of course, this can be infinite.
When one is modeling with a distribution that has infinite first or second moment, and one has practical questions where infinite first or second moment provides some obstruction, is there some remediation? Is there some common practice for reaching meaningful answers while circumventing the lack of moments?
