Co-Monotonicity of Optimal Investments and the Design of Structured Financial Products

We prove that under very weak conditions optimal financial products have to be co-monotone with the inverted state price density. Optimality is meant in the sense of the maximization of an arbitrary preference model, e.g. Expected Utility Theory or Prospect Theory. The proof is based on methods from transport theory. We apply the general result to specific situations, in particular the case of a market described by the Capital Asset Pricing Model, where we derive an extension of the Two-Fund-Separation Theorem. We use our results to derive a new approach to optimization in wealth management, based on a direct optimization of the return distribution of the portfolio.We provide existence and non-existence results for optimal products in this framework. Finally we apply our results to the study of down-and-out barrier options, show that they are not optimal and describe a construction of a cheaper product yielding the same return distribution