Computing Semiparametric Bounds on the Expected Payments of Insurance Instruments via Column Generation

It has been recently shown that numerical semiparametric bounds on the expected payoff of financial or actuarial instruments can be computed using semidefinite programming. However, this approach has practical limitations. Here we use column generation, a classical optimization technique, to address these limitations. From column generation, it follows that practical univariate semiparametric bounds can be found by solving a series of linear programs. In addition to moment information, the column generation approach allows the inclusion of extra information about the random variable, for instance, unimodality and continuity, as well as the construction of corresponding worst/best-case distributions in a simple way.