Optimal Product Design: A CAPM approach

We study properties of structured financial products optimizing a utility functional of a customer. The conventional method may have the disadvantage that the a priori restriction to a certain number of assets could make it impossible to find the optimal portfolio. So instead of optimizing the distribution of given assets, we impose only the price constraint as given by the CAPM and optimize the return distribution. In particular on nowadays markets where a multitude of asset types is available, it seems helpful to optimize first in the general framework, assuming a complete market, and then to find assets whose return distribution and conjoint probability distribution with the market portfolio resemble the theoretically optimal portfolio as closely as possible. We introduce a method to construct such optimal portfolios numerically and present some results for the cases of expected utility and cumulative prospect theory.