Borch's theorem from the perspective of comonotonicity
The paper deals with Borch's theorem on the characterization of Pareto optimal risk exchange treaties under the expected utility paradigm (in the framework of risk allocation the Pareto optimality means that it is impossible to improve the wellbeing of one trader without worsening the wellbeing of at least one other trader). Instead of optimizing by means of the traditional Lagrangian method or variational arguments the paper proposes a new method based on a Breeden-Litzenberger integral representation formula which allows to rewrite the objective function into a sum of mixtures of stop-loss transforms of the risk allocations. Moreover, this sum can be optimized applying the theory of comonotonicity. This approach enables e.g. to derive a closed-form expression for the given problem including the classical Borch's theorem and other interesting results.
scientific article; zbMATH DE number 6306784
scientific article