Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions

The structure of many models in economics and finance depends on majorization properties of convolutions of distributions. In this paper, we analyze robustness of these properties and the models based on them to heavy-tailedness assumptions. We show, in particular, that majorization properties of linear combinations of log-concavely distributed signals are reversed for very long-tailed distributions. As applications of the results, we study robustness of monotone consistency of the sample mean, value at risk analysis and the model of demand-driven innovation and spatial competition as well as that of optimal bundling strategies for a multiproduct monopolist in the case of an arbitrary degree of complementarity or substitutability among the goods. The implications of the models remain valid for not too heavy-tailed distributions. However, their main properties are reversed in the very thick-tailed setting